An object with mass 0.230 kg is acted on by an elastic restoring force with forc

Question

An object with mass 0.230 kg is acted on by an elastic restoring force with force constant 10.8 N/m . The object is set into oscillation with an initial potential energy of 0.140 J and an initial kinetic energy of 6.80×10?2 J . a) What is the amplitude of oscillation? A = 0.196 m b) What is the potential energy when the displacement is one-half the amplitude? U = 5.20*10^-2 J c) At what displacement are the kinetic and potential energies equal? x = 0.139 m d) What is the value of the phase angle ? if the initial velocity is positive and the initial displacement is negative? ? = ??? rad

Explanation / Answer

Here ,

mass of object , m = 0.230 Kg

force constant , k = 10.8 N/m

initial potential energy , PEi = 0.140 J

initial kinetic energy , KEi = 6.8 *10^-2 J

a) let the amplitude is A

0.5 * k * A^2 = PEi + KEi

0.5 * 10.8 * A^2 = 0.140 + 6.8 *10^-2

A = 0.196 m

the amplitude of oscillation is 0.196 m

b) at the one half of the amplitude

PE = 0.5 * 10.8 * (0.196/2)^2

solving for KE

KE = 5.2 *10^-2 J J

c)

for KE = PE

0.5 * 10.8 * (x)^2 = (0.140 + 6.8 *10^-2)/2

x = 0.139 m

d)

let the initial position is x

0.5 * k * x^2 = 0.140

0.5 * 10.8 * x^2 = 0.140

x = 0.161 m

initial phase angle = arcsin(x/A)

initial phase angle = arcsin(0.161/0.196)

initial phase angle = 0.94 radian

the phase angle is 0.94 radian

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