Question

1. An object-spring system moving with simple harmonic motion (SHM) has an amplitude A.

(a) What is the total energy of the system in terms of k and A only?

(b) Suppose at a certain instant the kinetic energy is twice the elastic potential energy, KE = 2PE. Re-write this equation by using only the variables for the mass, m, velocity, v, spring constant, k, and position, x.

(c) Using the results of (a) and (b) and conservation of energy, find the values of x, the positions of the object, when its kinetic energy equals twice the potential energy stored in the spring. Your answer must be in terms of A only. (i.e. A is the only variable that can appear in your answer.)

Answer #1

5. A mass attached to a spring
undergoes a simple harmonic motion (SHM) on a frictionless
horizontal surface. Suppose you increase the amplitude of the SHM,
which of the following quantities DOES (DO)
NOT increase? (There can be more than one answer)
1. The period of the SHM
2. The maximum acceleration
3. The frequency of the SHM
4. The maximum kinetic energy
5. The maximum spring potential
energy
6. The maximum speed.

A toy of mass 0.150 kg is undergoing simple harmonic motion
(SHM) on the end of a horizontal spring with force constant 300 N/m
. When the object is a distance 1.25×10?2 m from its equilibrium
position, it is observed to have a speed of 0.305 m/s .
a) What is the total energy of the object at any point of its
motion?
b) What is the amplitude of the motion?
c) What is the maximum speed attained by the...

if the amplitude of the simple harmonic motion of a mass-spring
system is doubled, the mechanical energy of the system:
a. decreases by a factor of 2
b. increases by a factor of 2
c. increases by a factor of sqrt(2)
d. increases by a factor of 4
e. decreases by a factor of 4.
f. decreases by a factor of sqrt(2)
g. does not change

A toy of mass 0.155 kg is undergoing simple harmonic motion
(SHM) on the end of a horizontal spring with force constant 305 N/m
. When the object is a distance 1.25×10−2 m from its
equilibrium position, it is observed to have a speed of 0.300 m/s
.
Part A) What is the total energy of the object
at any point of its motion?
E = ? J
Part B) What is the amplitude of the
motion?
A = ?...

A 1500 gram mass moving in a simple harmonic motion (SHM) passes
through the equilbrium point (x=0) with a spped of 2.60m/s. The
spring compresses and reaches a maximum displacement of 11.0
cm:
a. Calculate its spring constant by using consv. of energy
b. Calculate the period and frequency.
c. What is its velocity at T=10 seconds?
d. What is the maximum force that spring exerts on the block
during its motion? Where does this max force occur?

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=12kx2,
where k is the force constant of the spring and
x is...

The position of a certain system with mass of 10 kg exhibits
simple harmonic motion, where x(t) = 20 cos(15.2t + ?/4) and is in
units of meters. (a) What is the total energy of the system (let
the potential energy be zero at the equilibrium position)? (b) At t
= 0, what is the potential energy? (c) Kinetic energy?
Please answer with the concept of SHM

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 = ±

An object of 200,000 g is attached to a spring and executes a
simple harmonic motion with a period of 0.650 s. If the total
energy of the system is 8,700 J, find (a) the maximum speed of the
object, (b) the force constant of the spring and (c) the amplitude
of the movement.
a
6.595 m/s, 18.688 N/m, 1.197 m
b
9.327 m/s, 12.147 N/m, 0.965 m
c
9.327 m/s, 18.688 N/m, 0.965 m
d
6.595 m/s, 18.688 N/m,...

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

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