Simple Harmonic Motion 3 Question 2

2. A simple harmonic motion is represented by y=5(sin3πt+3cos3πt)cm. The amplitude and time period of the motion are

(a) 10cm,32s

(b) 5cm,23s

(c) 5cm,32s

(d) 10cm,23s

(2019 Main, 12 Jan II)

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Answer:

Correct Answer: 2. (d)

Solution:

  1. Equation for SHM is given as

y=5(sin3πt+3cos3πt)=5×212×sin3πt+32cos3πt=5×2cosπ3sin3πt+sinπ33πt=5×2sin3πt+π3[ using, sin(a+b)=sinacosb+cosasinb]

 or y=10sin3πt+π3

Comparing this equation with the general equation of SHM, i.e.

y=Asin2πtT+φ

We get, amplitude, A=10cm

and 3π=2πT

or Time period, T=23s



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