Out of the following functions, which represent/s SHM? I . y = sin ωt - cos ωt II . y = sin 3 ωt III . y = 5 cos 3 π 4 - 3 ωt IV . y = 1 + ωt + ω 2 t 2

Only (IV) does not represent SHM

Which one of the following equations of motion represents simple harmonic motion where k, k 0 , k 1, and a are all positive?

Acceleration = -k 0 x + k 1 x 2

Physics - Oscillations - Quiz-4

Two simple harmonic motions of angular frequencies 100 and 1000 rad s^-1 have the same displacement amplitude. The ratio of their maximum acceleration is:

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1: 10
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1: 10²
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1: 10³
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1: 10⁴

Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 s and the velocity of the wave is 300 m/s. What is the phase difference between the oscillations of two points?

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$\frac{π}{3}$
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$\frac{2 π}{3}$
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$π$
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$\frac{π}{6}$

A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:

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$\frac{T}{4}$
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$\frac{T}{8}$
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$\frac{T}{12}$
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$\frac{T}{2}$

A particle executing simple harmonic motion has a kinetic energy K₀cos²ωt. The values of the maximum potential energy and the total energy are, respectively,

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$0 a n d 2 K_{0}$
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$\frac{K_{0}}{2} a n d K_{0}$
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$K_{0} a n d 2 K_{0}$
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$K_{0} a n d K_{0}$

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?
(Take g = 10 m/s²)

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8.0 cm
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10.0 cm
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Any value less than 12.0 cm
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4.0 cm

The displacement of a particle executing simple harmonic motion is given by,

$y = A_{0} + A \sin ω t + B \cos ω t .$
Then the amplitude of its oscillation is given by:

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$A + B$
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$A_{0} + \sqrt{A^{2} + B^{2}}$
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$\sqrt{A^{2} + B^{2}}$
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$\sqrt{A_{0}^{2} + (A + B)^{2}}$

The average velocity of a particle executing SHM in one complete vibration is:

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zero
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$\frac{A ω}{2}$
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$A ω$
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$\frac{A ω^{2}}{2}$

Two pendulums (with the same angular amplitudes) of time periods 3s and 7s respectively start oscillating simultaneously from two opposite extreme positions with the same angular amplitudes. After how much time they will be in phase?

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$\frac{21}{8} s$
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$\frac{21}{4} s$
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$\frac{21}{2} s$
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$\frac{21}{10} s$

The amplitude of velocity of a particle is given by, $V_{m} = V_{0} / ({aω}^{2} - bω + c)$ where $V_{0}, a, b, c$ are positive:

The condition for a single resonant frequency is

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$b^{2} < 4 ac$
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$b^{2} = 4 ac$
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$b^{2} = 5 ac$
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$b^{2} = 7 ac$

Two pendulums have time periods T and 5T/4. They start SHM at the same time from the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation?

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$45 °$
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$90 °$
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$60 °$
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$30 °$

A simple harmonic oscillator has amplitude 'a' and time period T. The time required by it to travel from x=a to $x = \frac{a}{2}$ is

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$\frac{T}{6}$
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$\frac{T}{4}$
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$\frac{T}{3}$
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$\frac{T}{2}$

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is the maximum speed?

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100 m/min
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200 m/min
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300 m/min
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50 m/min

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40 cm. The block just loses contact with the plank when the later is momentarily at rest. Then

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the period of oscillation is $2 π / 3$
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the block weighs double its weight when the plank is at one of the positions of momentary at rest.
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the block weighs 1.5 times its weights on the plank halfway down
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the block weighs more than its true weight on the plank when the latter moves fastest

A body has a time period $T_{1}$ under the action of one force and $T_{2}$ under the action of another force, the square of the time period when both the forces are acting simultaneously in the same direction is

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$T_{1}^{2} T_{2}^{2}$
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$2 T_{1}^{2} T_{2}^{2}$
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$T_{1}^{2} + T_{2}^{2}$
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$T_{1}^{2} T_{2}^{2} / (T_{1}^{2} + T_{2}^{2})$

Motion of an oscillating liquid column in a U-tube is:

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periodic but not simple harmonic
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non-periodic
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simple harmonic and time period is independent of the density of the liquid
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simple harmonic and time-period is directly proportional to the density of the liquid

This time period of a particle undergoing SHM is 16s. It starts motion from the mean position. After 2s, velocity is $0.4 {ms}^{- 1}$ . The amplitude is:

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1.44m
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0.72m
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2.88m
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0.36m

A particle is performing simple harmonic motion along the x-axis with amplitude 4 cm and time period 1.2 s. The minimum time taken by the particle to move from x=+2 cm to x=+4cm and back again is given by:

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0.4 sec
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0.3 sec
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0.2 sec
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0.6 sec

The acceleration of a particle performing SHM is $12 cm \sec^{- 2}$ at a distance of 3 cm from the mean position. Its time period is:

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2.0s
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3.14s
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0.5s
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1.0s

The acceleration $d^{2} x / {dt}^{2}$ of a particle varies with displacement x as $\frac{d^{2} x}{d t^{2}} = - k x$

where k is a constant of the motion. The time period T of the motion is equal to :

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$2 πk$
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$2 π \sqrt{k}$
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$2 π / \sqrt{k}$
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$2 π / k$

A coin is placed on a horizontal platform, which undergoes horizontal SHM about a mean position O. The coin placed on the platform does not slip, the coefficient of friction between the coin and the platform is $μ$ . The amplitude of oscillation is gradually increased. The coil will begin to slip on the platform for the first time:

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at the mean position
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at the extreme position of oscillations
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for an amplitude of $μg / ω^{2}$
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for an amplitude of $g / {μω}^{2}$

A particle moves according to the law, $x = r \cos \frac{πt}{2}$ . The distance covered by it in the time interval between t=0 to t=3 s is:

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r
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2r
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3r
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4r

A particle is executing SHM of period 24 sec and of amplitude 41 cm with O as equilibrium position. The minimum time in seconds taken by the particle to go from P to Q, where OP=-9cm and OQ=40cm is:

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7
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9
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5
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6

The figure shows the circular motion of a particle which is at the topmost point on the y-axis at t=0. The radius of the circle is B and the sense of revolution is clockwise. The time period is indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is:

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x(t) = Bsin $(\frac{2 πt}{30})$
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x(t) = Bcos $(\frac{πt}{15})$
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x(t) = Bsin $(\frac{πt}{15} + \frac{π}{2})$
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x(t) = Bcos $(\frac{πt}{15} + \frac{π}{2})$

A $1.00 \times 10^{- 20} k g$ particle is vibrating with simple harmonic motion with a period of $1.00 \times 10^{- 5} s$ and a maximum speed of $1.00 \times 10^{3} m / s$ . The maximum displacement of the particle from the mean position is:

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(1) 59 mm
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(2) 1.00 cm
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(3) 10 m
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(4) None of these

Which one of the following equations does not represent SHM, x = displacement, and t = time? Parameters a, b and c are the constants of motion.

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x = a sin bt
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x = a cos bt + c
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x = a sin bt + c cos bt
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x = a sec bt + c cosec bt

The bob of a simple pendulum of length L is released at time t = 0 from a position of small angular displacement. Its linear displacement at time t is given by :

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$X = a \sin 2 π \sqrt{\frac{L}{g}} \times t$
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$X = a \cos 2 π \sqrt{\frac{g}{L}} \times t$
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$X = a \sin \sqrt{\frac{g}{L}} \times t$
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$X = a \cos \sqrt{\frac{g}{L}} \times t$

Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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