Question

A mass of 100 g is attached to a spring and oscillating with
simple harmonic motion. The position of the mass at all times is
given by

*x*(*t*) = (2.0 cm) cos(2*t*),

where *t* is in seconds, and the 2 is in rad/s. Determine
the following:

(a) The amplitude (in cm).

cm

(b) The frequency.

Hz

(c) The maximum speed in **cm/s**. Think about the
expression you can write for *v*(*t*). Where is the
maximum velocity in that expression? You can also use energy to
find the maximum speed.

(d) The velocity at *t* = 2.51 s. HINT: Use the information
you have found already to write out the expression for
*v*(*t*). Then evaluate your expression at *t*
= 2.51 s. NOTE that your answer should be in
**cm/s**

cm/s

(e) In which direction is the mass moving at this time?
---Select---neither, it is at a turnaround pointin the negative x
directionin the positive x direction

Answer #1

a) from the displacement equation

A= 2 cm

b) angular frequency from the displacement equation is,

=2 rad/s

f=2/(2*) = 0.3184 Hz

c) v= -A*sin(t) =
-Asqrt(1-cos^{2}(t))
{differentiating the displacement expression with respect to
time}

v= -*sqrt(A^{2}-x^{2})

now looking at the above expression we can say that velocity is maximum when x=0

v_{max} = -A = -2*2

v_{max} =-4 cm/s {negative sign tells us that the
direction of velocity is opposite to that of displacement}

d) v= -A*sin(t) = -2*2*sin(2*2.51)

v=3.8122 cm/s

e) since the velocity is positive hence it must be in the negative x direction

A mass of 187 g is attached to a spring and set into simple
harmonic motion with a period of 0.286 s. If the total energy of
the oscillating system is 6.94 J, determine the following.
(a) maximum speed of the object
m/s
(b) force constant
N/m
(c) amplitude of the motion
m

A block of mass 21.50 g on the end of spring undergoes
simple harmonic motion with a frequency of 6.00 Hz.
1. What is the spring constant of the spring?
2. If the motion of the mass has an initial amplitude of 7.00
cm what is its maximum speed?.
3. The amplitude decreases to 1.417 cm in 0.83
s, what is the damping constant for the system?

A simple harmonic oscillator has a frequency of 11.1 Hz. It is
oscillating along x, where x(t) = A cos(ωt + δ). You are given the
velocity at two moments: v(t=0) = 1.9 cm/s and v(t=.1) = -18.1
cm/s.
1) Calculate A.
2) Calculate δ.

A block attached to the end of a spring moves in simple harmonic
motion according to the position function where the
period of the motion is 4.0 s and the amplitude of the motion is 15
cm.
g) Determine the first time at which the position of the block
is -1.2 cm. ______ s
h) Determine the first time at which the velocity of the block
is -8.5 cm/s. ______ s
i) Determine the first time at which the acceleration of...

A simple harmonic oscillator consists of a mass of 100g attached
to a constant spring is 10^4 dynas/cm. At time t=0, the mass is
about 3 cm from the equilibrium point and with an initial velocity
of 5cm/s, both in the positive direction.A dissipative force is now
added. Assume that you start moving from rest at the maximum
amplitude position, and after oscillating for 10 s, your maximum
amplitude is reduced to half of the initial value. Calculate:
A- dissipation...

A) A mass on a spring vibrates in simple harmonic motion at a
frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is
started when its displacement from equilibrium is a maximum (hence
x = 8 cm when t = 0), what is the displacement of the mass when t =
3.7 s?
B) A mass of 4.0 kg, resting on a horizontal, frictionless
surface, is attached on the right to a horizontal spring with
spring...

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.

An object with mass 3.8 kg is executing simple harmonic motion,
attached to a spring with spring constant 260 N/mN/m . When the
object is 0.017 mm 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.

A metal ball attached to a spring moves in simple harmonic
motion. The amplitude of the ball's motion is 11.0 cm, and the
spring constant is 5.50 N/m. When the ball is halfway between its
equilibrium position and its maximum displacement from equilibrium,
its speed is 27.2 cm/s.
(a) What is the mass of the ball (in kg)?
(b) What is the period of oscillation (in s)?
(c) What is the maximum acceleration of the ball? (Enter the
magnitude in...

An object with mass 2.3 kg is executing simple harmonic motion,
attached to a spring with spring constant 330 N/m . When the object
is 0.020 m from its equilibrium position, it is moving with a speed
of 0.50 m/s . Part A Calculate the amplitude of the motion. Part B
Calculate the maximum speed attained by the object.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 46 minutes 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

asked 4 hours ago

asked 4 hours ago

asked 4 hours ago