Question

The displacement of an object at any instant of time executing shm is given as , x(t) = 1.2 cos [(2.3 π)t π/3], where x is in meter and t is in second. What is the velocity of the object at t = 0.5 s?

Answer 1

To find the velocity of an object in SHM at t = 0.5 s, one must use the formula v(t) = -Aω sin (ωt + ψ) with known amplitude, angular frequency, and time values, eventually calculating the sine term to obtain velocity in m/s.

Step-by-step explanation:

The question asks us to calculate the velocity of an object in simple harmonic motion (SHM) at a specific time. The displacement is given by x(t) = 1.2 cos [(2.3 π)t + π/3]. Using the general formula for SHM velocity, which is v(t) = -Aω sin (ωt + ψ), where ω is the angular frequency and ψ is the phase shift, we can find the velocity at t = 0.5 seconds.

Here, the amplitude A is 1.2 m, and the angular frequency ω is 2.3π s-1. Plugging these values and t = 0.5 s into the velocity formula, we get:

v(0.5) = -1.2 × 2.3 π sin [(2.3 π × 0.5) + π/3].

Calculating this expression will give us the velocity at t = 0.5 s. Remember that the unit of velocity will be meters per second (m/s).