Question

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 cos (pt). The magnitude of the acceleration (in m/s��) of the body at t = 1.0 s is approximately

Answer 1

The magnitude of the acceleration of the body at t = 1.0 s in simple harmonic motion is approximately -100π² m/s².

Step-by-step explanation:

The displacement of a body undergoing simple harmonic motion is given by the equation x(t) = X cos(pt). In this equation, X represents the amplitude of the motion and p represents the angular frequency. The magnitude of acceleration can be found using the equation a(t) = -p^2 X cos(pt). At t = 1.0 s, we can substitute the value of t into the equation to find the magnitude of acceleration.

Given x(t) = 5.0 cos(pt), we have X = 5.0 and p = 2π. Substituting these values into the equation for acceleration, we get:

a(t) = -p^2 X cos(pt) = - (2π)^2(5.0) cos(2πt) = - 4π^2 x 5.0 cos(2π) ≈ - 100π^2 m/s².