A mass of 25 kg is attached to the end of a spring that is s

A mass of 2.5 kg is attached to the end of a spring that is stretched 17 cm by a force of 15 N. It is set in motion with an initial position x_0 = 0 and initial velocity (in m/s) v_0 = = 6. Find the amplitude, period, and frequency of the resulting motion. You should assume that the system is frictionless.

Solution

Let, k be spring constant

Force of 15 N stretches is by .17 m

So, k=15/0.17=1500/17 N/m

angular frequency, w=sqrt{k/m}=sqrt{1500/(17*2.5)}~5.94 radians per second

Time period , T is given by

2\\pi/w~ 1.0576 s

Frequencey, f=w/(2 pi)~0.9455 Hz

Let amplitude of displacement be A

Then amplitude of velocity is Aw=6

A=6/w=6/sqrt{1500/(17*2.5)}~1.01 m