Question

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?

Answer #1

In an engine, a piston oscillates with simple harmonic motion so
that its position varies according to the expression, x = 7.00
cos(3t + π/7) 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/s^2
(d) Find the period and amplitude of the...

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.

An object executes simple harmonic motion with an amplitude A.
(Use any variable or symbol stated above as necessary.)
(a) At what values of its position does its speed equal half its
maximum speed? x = ±
(b) At what values of its position does its potential energy
equal half the total energy? x = ±

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 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....

An object in simple harmonic motion is oscillating about the
origin on the x-axis. At time t = 0 It is located
at x = 5 cm, and is moving to the left. If its maximum
oscillation amplitude A is 10 cm, what is the value of the
phase constant ϕ0?

A particle moving along the x axis in simple harmonic motion
starts from its equilibrium position, the maximum value, at t = 0,
moving to the right. The amplitude of the motion is 2.00 cm and the
frequency is 1.50 Hz. (a) Find an expression for the position of
the particle as a function of time. Determine (b) the maximum speed
of the particle and (c) the earliest time (t > 0) at which the
particle has this speed. Find...

An object is in simple harmonic motion with an amplitude of 20
mm and a period of 0.2 s.
1) What is its speed when its displacement from its equilibrium
position is 5 mm
2) What is its displacement when its speed is 0.5 m/s

An object with mass 2.8 kg is executing simple harmonic motion,
attached to a spring with spring constant 320 N/m . When the object
is 0.021 m from its equilibrium position, it is moving with a speed
of 0.65 m/s . Calculate the amplitude of the motion. Calculate the
maximum speed attained by the object.

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?
cm/s

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