Question

A particle is executing simple harmonic motion, Its displacement is given by x=5 sin $\pi$t, where x is in cm and t in seconds. How long will the particle take to move from the position of equilibrium to the position of maximum displacement?

• A. 0.5 s
• B. 1.0 s
• C. 1.5 s
• D. 2.0 s

Answer 1

The correct option is A 0.5 s

Maximum displacement = amplitude = 5 cm
At time t = 0, x = 0 (equilibrium position). Hence time t taken by the particle to move form X = 0 to x = 5 cm is given by
5 = 5 sin $\pi$ t
or, 1 = sin $\pi$ t
or $\pi$ t = $\frac{\pi }{2}$ or t = 0.5s