Question

The displacement of an object at any instant of time executing shm is given as, x(t) = 1.2 cos [(1.2 π) t π/3], where x is in meter and t in seconds. What is the velocity of the object at t = 0.2 s?

Answer 1

The velocity of the object at t = 0.2 s can be found using the differentiation of the displacement equation for simple harmonic motion.

Step-by-step explanation:

The displacement of an object in simple harmonic motion (SHM) is given by the equation x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time in seconds, and φ is the phase shift. In this case, the displacement equation is x(t) = 1.2 cos[(1.2π)t π/3]. To find the velocity at t = 0.2 s, we differentiate the displacement equation with respect to time. The velocity equation is v(t) = -Aω sin(ωt + φ). Substituting the given values and t = 0.2 s, we get v(t = 0.2 s) = -1.2π(1.2) sin[(1.2π)(0.2) π/3]. Calculate the expression to find the velocity at t = 0.2 s.