Question

An object is in simple harmonic motion. Its maximum position is 0.5 cm from equilibrium. It has an angular frequency of ?/2 rad/s.

Initially, ?(0)=(√2)/4 ?? and ?(0)=((√2)/8)? ??/s.

a) Use the values given above to write the function x(t) that describes the object’s position.

b) Write down the function v(t) that describes the object’s velocity.

c) Write down the function a(t) that describes the object’s acceleration.

d) Draw a velocity versus time graph showing two cycles of the motion. Be sure both axes are labeled with numerical values. Explain how you used each of the given values in drawing your graph.

e) Draw an acceleration versus time graph showing two cycles of the motion. Be sure both axes are labeled with numerical values.

Answer #1

The position of an object in simple harmonic motion as a
function of time is given by ? = 3.8??? (5??/4 + ?/6) where t is in
seconds and x in meters. In t = 2.0s calculate (a) the period, (b)
the oscillation frequency (c) velocity and (d) acceleration.

A particle moving along the x axis in simple harmonic motion
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In an engine, a piston oscillates with simple harmonic motion so
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(a) At t = 0, find the position of the piston. ____ cm
(b) At t = 0, find velocity of the piston. ____ cm/s
(c) At t = 0, find acceleration of the piston. ____ cm/s^2
(d) Find the period and amplitude of the...

In an engine, a piston oscillates with simple harmonic motion so
that its position varies according to the expression,
x = 8.00 cos (3t + pi/4)
where x is in centimeters and t is in
seconds.
(a) At t = 0, find the position of the piston.
cm
(b) At t = 0, find velocity of the piston.
cm/s
(c) At t = 0, find acceleration of the piston.
cm/s2
(d) Find the period and amplitude of the motion.
period...

An object is undergoing simple harmonic motion along the x-axis.
its position is described as a function of time by x(t)=
5.3cos(4.2t-1.9), where x is in meters, the time t, is in seconds,
and the argument of the cosine is in radians.
c) determine the position of the object, in meters, at the time
t=2.6s?
d) what the objects velocity, in meters per second, at the time
t=2.6s?
e) calculate the objects acceleration, in meters per second
squared, at time...

An object undergoes simple harmonic motion along the x-axis with
a period of 0.5 s and an amplitude of 25 mm. Its position is x = 14
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your logbook write an equation of motion with all the variables
identified and sketch a graph of position vs. time for the
oscillator. What is the initial phase? [Work in rotational
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The position of an object in simple harmonic motion is given by
x= (6.88 cm) cos [(2 pie/0.663 s)t]
(a) What is the object's speed at 0.828 s?
cm/s
(b) What is the object's maximum speed?
cm/s
(c) What is the object's speed when -6.88 cm?
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Simple Harmonic Motion
The velocity is maximum when the position is ______?
The acceleration is maximum when the position is _______?
The net force is maximum when the position is _________?
True/ False : The gravitational force on the mass is zero at
themaximum in position.
True/False: the gravitational force on the mass is zero at
theequilibrium position.
True/False: the force exerted by teh spring is zero at
theequilibrium position.
True/Fase: teh net force on the mass is zero at...

For an object with simple harmonic motion;
a) What can you say about its speed, acceleration and kinetic
energy at equilibrium?
b) For simple harmonic motion given by x = 3,8 cos (5πt / 4 + π / 6), what is its amplitude, frequency, position and speed for t = 0?

A mass on a spring undergoes simple harmonic motion. At t = 0
its displacement is 1m and its velocity is 1m/s towards the
equilibrium position. What single piece of information allows you
to determine the displacement at time t = 1 s?
A. mass
B. spring constant (k)
C. kinetic energy at t = 0
D. acceleration at t = 0
E. force at t = 0

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