A mass of 0.24 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.24 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by

x(t) = (0.40 m)cos[(16 rad/s)t].

Determine the following.

(a) amplitude of oscillation for the oscillating mass
  m .40m (this was correct)

(b) force constant for the spring
  N/m 61.44 N/m (this was correct)

(c) position of the mass after it has been oscillating for one half a period
How long does it take the oscillating mass to travel from the maximum positive displacement to the maximum negative displacement? m

(d) position of the mass one-third of a period after it has been released
m

(e) time it takes the mass to get to the position

x = ?0.10 m after it has been released

s

Explanation / Answer

In general, x(t) = A cos(?t - ?), where A is the amplitude, ? is the angular frequency, and ? is some phase shift.

(a)
0.40 m

(b)
For the spring-mass system,
?

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