Topic: Theory of Machines and Vibrations
Oscillation of a particle is prescribed by the equation $x=3~cos~0.25~\pi t$. Where t is the time in seconds. Then time taken by the particle to move from position of equilibrium to maximum displacement is
- A. 0.5 sec
- B. 1.0 sec
- C. 2.0 sec
- D. 3.0 sec
Answer: C. 2.0 sec
Explanation: Comparing with the standard SHM equation $x = A\cos(\omega t)$, we get $\omega = 0.25\pi$. Time period $T = \frac{2\pi}{\omega} = \frac{2\pi}{0.25\pi} = 8~sec$. The time taken to move from the position of equilibrium to maximum displacement is one quarter of the time period, $t = \frac{T}{4} = \frac{8}{4} = 2~sec$.