Question

For an object in simple harmonic motion with amplitude a and period 2/π, find an equation that models the displacement y at time t.

a) y= a cos(π/2t)
b) y= a sin(πt)
c) y= a cos(πt)
d) y= a sin(2π/t)

Answer 1

For an object with amplitude a and period 2/π in simple harmonic motion, the displacement y at time t is best described by the equation y = a cos(πt), which is option c.

Step-by-step explanation:

For an object undergoing simple harmonic motion (SHM) with amplitude a and period 2/π, the displacement y at time t can be modeled by either a sine or cosine function, as both represent SHM. Given the period of the motion which is 2/π, we can determine the angular frequency ω as ω = 2π/T.

In this case, T is the period, so ω = π. The displacement can be written in the form y(t) = a cos(ωt) or y(t) = a sin(ωt) depending on the initial conditions. Since no initial phase shift or starting position has been specified, both a sine and cosine function could potentially model the motion; however, typically in SHM, a cosine function represents starting at maximum displacement, which would be option c) y= a cos(πt).

The displacement in simple harmonic motion is given by the equation y = a cos(πt/2). Therefore, the correct answer is y = a cos(πt/2), option a).