Explanation
Hint: Here, we have to apply trigonometric formulas
Solution:
Step1: Simplify the given displacement
x=4(cosπt + sinπt).....(1)
Multiply & divide each term of R.H.S. of equation (1) by √2 we get,
⇒4√2×√2(cosπt +sinπt)
⇒4√2(1√2cosπt+1√2sinπt).....(2)
Step2: Apply required trigonometric formula we know that, 1√2=sinπ4 and 1√2=cosπ4
Now, equation (2) becomes,
⇒4√2(cosπtsinπ4+sinπtcosπ4).....(3)
Also, sin(a+b)=sinacosb+cosasinb
Now, equation (3) becomes,
x=4√2sin(πt +π4).....(4)
Step3: Find Amplitude ‘A’
Comparing above equation (4) with,
x=A(sinωt+Φ)
We get, Amplitude, A=4√2
Hence, option (C) is correct.
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