A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 sin ( $\pi$t + $\pi$/3).The velocity (in m/s)of the body at t = 1.0 s is
A)+7.9
B)-7.9
C)-14
D)+14
E)-5.0

Question

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 sin ( $\pi$t +  $\pi$/3).The velocity (in m/s)of the body at t = 1.0 s is
A)+7.9
B)-7.9
C)-14
D)+14
E)-5.0

Quizplus · Accepted Answer

The velocity of a body in simple harmonic motion is given by v(t) = dx/dt. Differentiating x = 5.0 sin(πt + π/3) with respect to t gives v(t) = 5.0π cos(πt + π/3). Substituting t = 1.0 s, we get v(1.0) = 5.0π cos(π + π/3) = -5.0π cos(4π/3) = -7.9 m/s.

A Body Oscillates with Simple Harmonic Motion Along the X π\piπ

A Body Oscillates with Simple Harmonic Motion Along the X $\pi$