Question

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.

Answer #1

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 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....

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?

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...

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 function
x = (4.8 m) cos[(3πrad/s)t + π/6
rad]
gives the simple harmonic motion of a body. At t = 5.6 s,
what are the (a) displacement,
(b) velocity, (c) acceleration,
and (d) phase of the motion? Also, what are the
(e) frequency and (f) period of
the motion?

The function x = (8.0 m) cos[(4πrad/s)t + π/5 rad] gives the
simple harmonic motion of a body. At t = 6.9 s, what are the (a)
displacement, (b) velocity, (c) acceleration, and (d) phase of the
motion? Also, what are the (e) frequency and (f) period of the
motion?

The function x = (9.5 m) cos[(6πrad/s)t + π/4 rad] gives the
simple harmonic motion of a body. At t = 2.3 s, what are the (a)
displacement, (b) velocity, (c) acceleration, and (d) phase of the
motion? Also, what are the (e) frequency and (f) period 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?

Astronomy:
1. Determine the position in the oscillation where an
object in simple harmonic motion:
a. has the greatest speed.
b. has the greatest acceleration.
c. experiences the greatest restoring
force.
d. experiences zero restoring force.
2. Describe simple harmonic motion, including its cause
and appearance.
3. Describe how the change in a. amplitude (angle), b.
length, and c. mass affect the period of the
pendulum.\
4. Do measurements including uncertainty fall within the
accepted value? Which method is more...

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