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An object of mass m = 0.25kg has a horizontal spring attached to its left side, and
slides along a frictionless surface. The spring constant is ? = 0.4 N . At t = 0s, the m
object is displaced 0.1m to the right of its equilibrium position. Its initial velocity is 0.4 m , toward the right.

a) What is the period T of the motion?
b) What is the angular frequency ? ?
c) What is the frequency ? ?
d) What is the total energy E ?
e) What is the amplitude A of the motion? (careful!)
f) What is the phase angle ? ?
g) What is the maximum velocity vmax? (careful!)
h) What is the maximum acceleration amax ?
i) What are the position, velocity, and acceleration at t = ? s?
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Given Data
mass m = 0.25 kg,
spring constant k = 0.4 N/m

at t=0
x = 0.1 m,
initial velocity = 0.4 m/s

a) T = 2pi *sqrt(m/k) = 2pi*sqrt(0.25 / 0.4)
T=6.28*sqrt(0.625)

T = 4.964 s

b )

w = 2pi/Time peroid=6.28/4.964

c)f = 1 / Time peroid = 1 / 4.964 = 0.201 Hz

d) E = 0.5kx^2 + 0.5mv^2

= 0.5 * 0.4 * 0.12 + 0.5 * 0.25 *0.42

E = 0.022 J

e) 0.5 * k * A2 = E

A = sqrt (2 * E / k) = sqrt (2 * 0.022 / 0.4)

A = 0.3316 m

g) 0.5 * m * Vmax2 = E

Vmax = sqrt( 2 * E / m) = sqrt( 2 * 0.022 / 0.25)

Vmax = 0.42

h) a = k * A / m = 0.528 m/s
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