The full question is: A 4.10 kg object on a horizontal frictionless surface is a

Question

The full question is: A 4.10 kg object on a horizontal frictionless surface is attached to a spring with spring constant 900 N/m. The object is displaced from equilibrium 50.0 cm horizontally (in the direction) and given an initial velocity of 10.1 m/s back toward the equilibrium point at t=0 s.

(a) What is the frequency of the motion?

(b) What is the initial potential energy of the block-spring system?

(c) What is the initial kinetic energy?

(d) What is the amplitude of the oscillation?

(e) Write down the equation: Please fill in the numerical values for A, ? and below, in SI units. Use a positive value.
x(t) = ?

Explanation / Answer

a)

w = k/m = 900/4.10 = 14.816 rad/s

f = w/2 = 2.35803 2.36 Hz

b)

0.5 k x^2 = 0.5 * 900 *0.50*0.50 = 112.5 J

c)

0.5 m v^2 = 0.5 * 4.10 * 10.1*10.1 = 209.1205 J

d)

0.5 k A^2 = 112.5 + 209.1205

0.5 * 900 * A^2 = 321.6205

A = 0.84541 0.845 m

e)

x(t) = 0.845 cos ( 14.816 t + )

0.5 = 0.845 cos ( 14.816 t + ) >>>> = 0.9376 rad

x(t) = 0.845 cos ( 14.816 t + 0.9376)

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