Question

The displacement of an object in simple harmonic motion is described by the equation 0.40m*sin(8.9rad/s(t)) + 0.61m*cos(8.9rad/s(t)).

A) Determine the position and velocity when t = 0 seconds.

B) Determine the maximum displacement of the system.

C) Determine the maximum acceleration of the system.

D) Determine the velocity of the system at t = 6 seconds.

Answer 1

The postion is given by s(t)

the velocity is given by v(t)

the accleration is given by a(t)

a) The positon at time t = 0 is

the velocity at t = 0 is

b) The maximum displacemnt of the system occurs when v = 0

putting the

= 0 we get t = 0.065 s

putting the value in

we get

c) The maximum accleration of the system occurs when v = 0

putting the

= 0 we get t = 0.065 s

putting the value in

d) The veloctity of the systme at t = 6 s we get

= -3.56 m/s