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# A simple harmonic motion is represented by y=5(sin3πt+√3cos3πt)cm The amplitude and time period of the motion are :10cm,23s10cm,32s5cm,23s5cm,32s

A
10cm,23s
B
5cm,23s
C
10cm,32s
D
5cm,32s
Solution
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#### y=5(sin3πt+√3cos3πt)y=5×2(12sin3πt+√32cos3πt)y=10(cosπ3sin3πt−sinπ3cos3πt)y=10sin(3πt+π3)Comparing it with y=Asin(ωt+ϕ)⇒A=10 i.e., amplitude is 10cm⇒T=2πω=2π3π=23 sec. i.e, time period is 23 sec.

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