Question

As you know, a common example of a harmonic oscillator is a mass
attached to a spring. In this problem, we will consider a
*horizontally* moving block attached to a spring. Note that,
since the gravitational potential energy is not changing in this
case, it can be excluded from the calculations.

For such a system, the potential energy is stored in the spring and is given by

*U*=12*k**x*2,

where *k* is the force constant of the spring and
*x* is the distance from the equilibrium position.

The kinetic energy of the system is, as always,

*K*=12*m**v*2,

where *m* is the mass of the block and *v* is the
speed of the block.

We will also assume that there are no resistive forces; that is,
*E*=constant.

A) Find the total energy of the object at any point in its motion.

B) Find the amplitude of the motion.

C) Find the maximum speed attained by the object during its motion.

Answer #1

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.

A simple harmonic oscillator consists of a 675-g block attached
to a lightweight spring. The total energy of the system is 9.40 J,
and its period of oscillation is 0.340 s.
(a) What is the maximum speed of the block?
Did you accidentally divide or take the inverse in your
calculation? m/s
(b) What is the force constant of the spring?
N/m
(c) What is the amplitude of the motion of the block?
m

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.

In Classical Physics, the typical simple harmonic oscillator is
a mass attached to a spring. The natural frequency of vibration
(radians per second) for a simple harmonic oscillator is given by
ω=√k/m and it can vibrate with ANY possible energy whatsoever.
Consider a mass of 135 grams attached to a spring with a spring
constant of k = 1 N/m. What is the Natural Frequency (in rad/s) of
vibration for this oscillator?
In Quantum Mechanics, the energy levels of a...

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.

An object with mass 3.6 kg is executing simple harmonic motion,
attached to a spring with spring constant 320 N/m . When the object
is 0.025 m from its equilibrium position, it is moving with a speed
of 0.40 m/s.
Part A: Calculate the amplitude of the motion.
Part B: Calculate the maximum speed attained by the object.

An object with mass 2.5 kg is attached to a spring with spring
stiffness constant k = 270 N/m and is executing simple harmonic
motion. When the object is 0.020 m from its equilibrium position,
it is moving with a speed of 0.55 m/s.
(a) Calculate the amplitude of the motion. ____m
(b) Calculate the maximum velocity attained by the object.
[Hint: Use conservation of energy.] ____m/s

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 spring-mass system consists of a 0.5 kg mass attached to a
spring with a force constant of k = 8 N/m. You may neglect the mass
of the spring. The system undergoes simple harmonic motion with an
amplitude of 5 cm. Calculate the following: 1. The period T of the
motion 2. The maximum speed Vmax 3. The speed of the object when it
is at x = 3.5 cm from the equilibrium position. 4. The total energy
E...

A simple harmonic oscillator consists of a block of mass 3.70 kg
attached to a spring of spring constant 410 N/m. When t = 1.60 s,
the position and velocity of the block are x = 0.102 m and v =
3.050 m/s. (a) What is the amplitude of the oscillations? What were
the (b) position and (c) velocity of the block at t = 0 s?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 24 minutes ago

asked 24 minutes ago

asked 27 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago