Question

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

a) Calculate the period T of the motion. b) Calculate the angular frequency ω. c) Calculate the frequency ν. d) Calculate the total energy E. e) Calculate the amplitude A of the motion. (careful!) f) Calculate the phase angle φ. g) Calculate the maximum velocity vmax. (careful!) h) Calculate the maximum acceleration amax. i) Calculate the position, velocity, and acceleration at t = π 8 s.

Answer #1

The position of a 0.30 kg object attached to a spring is
described by x = (0.25 m) cos(0.4 π t).
(a) What is the amplitude of the motion?
(b) Calculate the spring constant.
(c) Calculate the position of the object at t = 0.30 s.
(d) Calculate the velocity of the object at t = 0.30 s.

If the object-spring system is described by x = (0.340
m) cos (1.55t), find the following.
(a) the amplitude, the angular frequency, the frequency, and the
period
A =
m
ω =
rad/s
f =
Hz
T =
s
(b) the maximum magnitudes of the velocity and the
acceleration
vmax =
m/s
amax =
m/s2
(c) the position, velocity, and acceleration when t =
0.250 s
x =
m
v =
m/s
a =
m/s2

If the object-spring system is described by x = (0.315
m) cos (1.60t), find the following.
(a) the amplitude, the angular frequency, the frequency, and the
period
A=.315 m
w=1.6 rad/s
f=.25 HZ
T=3.9s
(b) the maximum magnitudes of the velocity and the
acceleration
vmax=.504 m/s
amax=.8064 m/s^2
(c) the position, velocity, and acceleration when t =
0.250 s
x= ?
v=?
a=?

If the object-spring system is described by x = (0.310
m) cos (1.55t), find the following.
(a) the amplitude, the angular frequency, the frequency, and the
period
A =
m
ω =
The angular frequency is ω in
Acosωt. rad/s
f =
Hz
T =
s
(b) the maximum magnitudes of the velocity and the
acceleration
vmax =
m/s
amax =
m/s2
(c) the position, velocity, and acceleration when t =
0.250 s
x =
m
v =
m/s
a...

The position of a 0.30 - kg object attached to a spring is
described by
x = (0.25 m) cos ( 0.4 π t ).
Find:
a) The amplitude of the motion;
b) Frequency and Period of the motion;
c) Position of the object at t = .30 sec.
d) Speed of the object at t = .30 sec.
e) Acceleration of the object at t = .30 sec

A 6.5-kg mass is attached to an ideal 750-N/m spring. If the
system undergoes simple harmonic motion, what are the frequency,
angular frequency, and period of the motion?
The frequency, f =
The angular frequency, ω =
The period, T =
If the total mechanical energy of the system is 72 J, what are
the amplitude, maximum speed and maximum acceleration of the
motion?
The amplitude, A =
The maximum speed, vmax =
The maximum acceleration, amax =

The position of a 0.30 - kg object attached to a spring is
described by
x = (0.25 m) cos ( 0.4 π t ). Find:
a) The amplitude of the motion;[2pt]
b) Frequency and Period of the motion;[4pt]
c) Position of the object at t = .30 sec.[3pt]
d) Speed of the object at t = .30 sec.[3pt]
e) Acceleration of the object at t = .30 sec.[3pt]

An object of mass (m = 0.8 kg) is attached to a horizontal
spring. Its position varies with time as x = (0.33
m)cos(0.2πt).
(a) Find the amplitude of its motion (in m).
(b) Find the spring constant (in N/m).
(c)Find the position (in m) at t = 0.2 s.
(d)Find the speed (in m/s) of the object at t = 0.2 s.

An object of mass of 2.7 kg is attached to a spring with a force
constant of k = 280 N/m.
At t = 0, the object is observed to be 2.0 cm from its equilibrium
position with a speed of
55 cm/s in the -x direction. The object undergoes simple harmonic
motion “back and
forth motion” without any loss of energy.
(a) Sketch a diagram labeling all forces on the object and
calculate the maximum
displacement from equilibrium of...

A spring of negligible mass stretches 3.00 cm from its relaxed
length when a force of 7.10 N is applied. A 0.440-kg particle rests
on a frictionless horizontal surface and is attached to the free
end of the spring. The particle is displaced from the origin to
x = 5.00 cm and released from rest at t = 0.
(Assume that the direction of the initial displacement is positive.
Use the exact values you enter to make later calculations.)
(a)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 2 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago