Question

An object moves up and down the y- axis with an acceleration gives as a function of time t by the expression a= A sin wt, where A and w are constants. What is the period of this motion?

Answer 1

The period of the motion described by the acceleration function a = A sin wt is determined by the angular frequency w, using the formula T = 2π/w, which is characteristic of simple harmonic motion.

Step-by-step explanation:

The period of the motion for an object whose acceleration is given by the function a = A sin wt, where A and w are constants, can be determined by the properties of simple harmonic motion (SHM). In SHM, the acceleration is directly proportional to the sinusoidal function of time, and from the given expression, w represents the angular frequency of the motion. The period, T, is related to angular frequency by the formula T = 2π/w.

Therefore, by understanding the relationship between period and angular frequency, one can solve for the period of this oscillatory motion.