Question

1. Motion repeated at regular intervals of time is called periodic. Explain the simple harmonic motion with a figure.

2. A particle executes a simple harmonic motion with a period 2 seconds, starting from its equilibrium at time t = 0. Find the minimum time in which it is displaced by half the amplitude.

Answer 1

1. A periodic motion in which acceleration is directly proportional to displacement but opposite in direction is called SHM.

The graphical variation of simple harmonic motion with time given above.

2. y = a sin wt

\(\frac{a}{2}\) = a sin wt

\(\frac{1}{2}\) = sin wt

Sin π/6 = sin wt

wt = π/6

\(\frac{2\pi}{T}\)t = π/6

But T = 2s. 

Hence we get

\(\frac{2\pi}{2} t = \pi/6\)

t = \(\frac{1}{6}\)s