A body of mass 0.50 kg moves in simple harmonic motion with a period of 1.5 s and an amplitude of 20 mm.Which of the following equations correctly represents this motion?
A)x = 40 cos(t/1.5)mm
B)x = 40 cos(2$\pi$t/1.5)mm
C)x = 20 sin(t/1.5)mm
D)x = 20 sin(1.5$\pi$t)mm
E)x = 20 sin(2$\pi$t/1.5)mm

Question

Quizplus · Accepted Answer

The equation for simple harmonic motion is given by x = A sin(2πft). In this case, the amplitude A is given as 20 mm and the period T is given as 1.5 s. Using the relation T = 1/f, we can find the frequency f as f = 1/T = 2/3 Hz. Substituting the values in the equation, we get x = 20 sin(2π(2/3)t) = 20 sin(4πt/3) = 20 sin(2πt/(3/2)). This matches the form x = 20 sin(2πft/1.5) given in option E. Therefore, the correct choice is E.

A Body of Mass 0 π\piπ T/15)mm C)x = 20 Sin(t/1 π\piπ

A Body of Mass 0 $\pi$ T/15)mm
C)x = 20 Sin(t/1 $\pi$