A mass of 0.44 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.44 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) = (0.20 m)cos[(18 rad/s)t]. Determine the following.

(A) Amplitude of oscillation for the oscillating mass

____ m?

(B) Force constant for the spring

____ N/m ?

(C) Position of the mass after it has been oscillating for one half a period

____ 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

compare the given equation with

x = A*cos(w*t)

we get

a)
A = 0.2 m

b)
w = 18 rad/s

w = sqrt(k/m)

==> k = w^2*m

= 18^2*0.44

= 142.56 N/m

c) x = -0.2 m

d) x = 0.2*cos(w*t)

= 0.2*cos(w*T/3)

= 0.2*cos(2*pi/T)*(T/3))

= 0.2*cos(2*pi/3)

= -0.1 m

e) t = T/3

= 2*pi/(w*3)

= 2*pi/(18*3)

= 0.116 s

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