Help finding frequency, period, velocity and maximum speed?

Question

A particle's displacement from equilibrium is given by x(t) = 0.43cos(3.5t + π/4), where x is in meters and t is in seconds.

(a) Find the frequency f and period T of its motion.

frequency _______ Hz

period _______ s

(b) Find an expression for the velocity of the particle as a function of time.

_______ (Use pi for π and t as necessary.)

(c) What is its maximum speed?

_______ m/s

Answer 1

The equation for simple harmonic motion is ;

x(t) = ACos(2Pi*f*t +Phi)

so the Frequency is f = 3.5/2Pi

the period is 1/f

Vmax = A*Omega

Omega = 2Pi*f

A = x(t)/(cos(2Pi*f*t+Phi)

Answer 2

a)  Frequency: 0.557 Hz (omega/2pi = 3.5/2pi)

Period: 1.795 seconds (1/f)

b) v(t) = -1.505sin(3.5t + pi/4)

c) 1.505 m/s

Answer 3

a)

Period: 2pi/3.5 = 1.8s

Frequency = 1/Period = 0.56 Hz

b)

x'(t) = v(t) = -0.43*3.5*sin(3.5t + pi/4) = -1.51sin(3.5t + pi/4)

c)

vmax = 0.43*3.5 = 1.51