Question

A 0.52·kg mass vibrates according to the equation *x* =
0.49 cos (8.37*t* + 3.54), where *x* is in meters,
and *t* is in seconds.

(a) Determine the amplitude.

m

(b) Determine the frequency.

Hz

(c) Determine the total energy.

J

(d) Determine the kinetic energy and potential energy when
*x* = 0.30 m.

kinetic energy =

J

potential energy = J

Answer #1

Here

part A)

as the equation of the simple harmonic motion is

x = A * cos(w * t + phi)

x = 0.49 cos (8.37t + 3.54

comparing the equations

Amplitude = A = 0.49 m

part B)

frequency = w/(2pi)

frequency = 8.37/(2pi)

frequency = 1.33 Hz

c)

for the total energy

total energy = 0.50 * m * Vmax^2

total energy = 0.50 * 0.52 * (0.49 * 8.37)^2

total energy = 4.37 J

d)

at x = 0.30 m

potential energy = total energy * x^2/A^2

potential energy = 4.37 * 0.30^2/0.49^2

**potential energy = 1.64 J**

for the kinetic energy

kinetic energy = 4.37 - 1.64

**kinetic energy = 2.73 J**

A 0.55·kg mass vibrates according to the equation x =
0.41 cos (8.41t + 1.52), where x is in meters,
and t is in seconds.
(a) Determine the amplitude. m
(b) Determine the frequency. Hz
(c) Determine the total energy.J
(d) Determine the kinetic energy and potential energy when
x = 0.29 m.
kinetic energy = J
potential energy = J

A 0.55·kg mass vibrates according to the equation x =
0.44 cos (8.41t + 4.83), where x is in meters,
and t is in seconds.
(a) Determine the amplitude.
m
(b) Determine the frequency.
Hz
(c) Determine the total energy.
J
(d) Determine the kinetic energy and potential energy when
x = 0.32 m.
kinetic energy =
J
potential energy =
J

A 0.45·kg mass vibrates according to the equation x =
0.45 cos (8.36t + 4.92), where x is in meters,
and t is in seconds.
(a) Determine the amplitude.
m
(b) Determine the frequency.
Hz
(c) Determine the total energy.
J
(d) Determine the kinetic energy and potential energy when
x = 0.35 m.
kinetic energy =
J
potential energy = J

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x=0.50cos6.80t, where x is in meters and t is in seconds.
A) Determine the amplitude.
B) Determine the frequency.
C) Determine the total energy
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Part D
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