Question

Suppose that a body of an object is experiencing SHM ( simple harmonic motion) and it oscillates with position x(t)=(0.55m)Cos(35s^-1t + pi)

a)What is the period, frequency, and angular frequency
b) calculate its initial velocity and the maximum speed it can have
C) calculate its initial acceleration and the maximum( in magnitude) of the acceleration
d) when the object is in 2.0s , what is its position and location

Answer 1

x = A cos (2 pi f t + pi}
but
cos (a+b) =cos a cos b -sin a sin b
so
x = A[ cos (2pift) cos pi - sin (2 pi f t) sin pi ]
but cos pi = -1 and sin pi = 0
so
x = -A oos 2 pi f t
x = -.55 cos 35 t

2 pi f = 35 = omega
2 pi/T = 35
f = 35/2pi

v = dx/dt = .55(35) sin 35 t
v = 0 at t = 0v = .55*35 max

a = .55* 35^2 cos 35 t
etc :)