Question

The equation of a simple harmonic motion of amplitude 10 units and time-period 2 units will be

(A) \(y = 10\sin \pi t\)

(B) \(y = 10\sin 2\pi t\)

(C) \(y = 0.1\sin 4\pi t\)

(D) \(y = 0.1\sin 2\pi t\)

Answer 1

Correct option is (A) \(y = 10\sin \pi t\)

The general equation of a S.H.M is,

\(y = A\sin wt\)

Given,

Amplitude (A) = 10 units

Time period (T) = 2 units

We know that,

\(T = \frac{2\pi}w\)

\(2= \frac{2\pi}w\)

we get, \(w = \pi\)

Now,

Substituting \(A = 10\) and \(w = \pi\) in \(y = A\sin wt\)

Therefore, \(y = 10\sin \pi t\)