A body with mass 250g is attached to the end of a spring that is stretched to 25

Question

A body with mass 250g is attached to the end of a spring that is stretched to 25cm by a force of 15N. At time t=0 the body is pulled 1m to the right, stretching the spring, and set in motion with an initial velocity of 5m/s to the left. The only force acting on the spring is the sprig restoring force and the governing law of motion is Newton's second law.

1. Find the IVP that represents the motion of the mass a function of time, for convenience, write W=the root of (k/m).

2. Find the position of the body as a function of time in the form x(t)=C cos(Wt-a).

3. FInd the amplitude, the frequency and the period of motion of the body and sketch its position graph.

Please answer with details and mark the question numbers.

Explanation / Answer

given

m = 0.250 kg, k = 9/0.25 N/m = 36 N/m, x(0) = 1 m, x'(0) = -5m/s

the differential equation is -kx = mx"

a)

x'' = -w^2*x
0.250x" + 36x = 0
x" + 144x = 0
b)

r2 + 144 = 0
r =

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.