1. A 0.25 kg harmonic oscillator has a total mechanical energy
of 4.1J. If the oscillation amplitude is 20.0cm. what is the
oscillation frequency?
2. A 0.250-kg stone is attached to an ideal spring and undergoes
simple harmonic oscillations with a period of 0.640 s. What is the
force constant (spring constant) of the spring?
3. An object of mass m = 8.0 kg is attached to an ideal spring
and allowed to hang in the earth's gravitational field. The...
Take an eigenfunction for the harmonic oscillator and the
corresponding energy eigenvalue, and substitute them into the
Schrodinger equation. Then prove that the equation is satisfied. Do
this for n =4, show how n is substituted.
Demonstrate that the WKB approximation yields the energy levels
of the linear harmonic oscillator and compute the WKB approximation
for the energy eigenfunctions for the n=0 and n=1 state and compute
with the exact stationary state solutions.
If the coefficient of kinetic friction is 0.2, what friction of
the total mechanical energy is lost due to frictional forces?
Run#
Mass of hanger + weights (M)
mass of glider +flag (m)
velocity of glider (v)
d (m)
potential energy lost (Mgd) (J)
Kinetic energy gained 1/2 (m+M)v2
% change (ME)
1
0.05
0.2118
0.88
0.235
0.1152675
0.10136896
12.05763984
2
0.07
0.2118
1.01
0.235
0.1613745
0.14373209
10.93258848
3
0.09
0.2118
1.12
0.235
0.2074815
0.18928896
8.768270906
4
0.11
0.2118
1.2...
1. Show that the Kinetic Energy and the Momentum are conserved
in this system. (Remember that momentum is a vector, so you need to
show the conservation of the momentum in x and y directions
separately.)
Data:
Before the collision: m1= 1kg v1x
=1 m/s v1y=0 m/s m2=1kg v2x=-1m/s
v2y=0 m/s
After the collision: m1= 1kg v1x
=-0.778 m/s v1y=-0.629 m/s m2=1kg
v2x= 0.778 m/s v2y=0.629 m/s
2. From the data, calculate the direction(angles) of the final
velocities of the...
Suppose the total mechanical energy of an object is conserved.
Which one or more of the following statements is/are true?
A) If the kinetic energy decreases, the gravitational potential
energy increases
B) If the gravitational potential energy decreases, the kinetic
energy increases
C) If the kinetic energy does not change, the gravitational
potential energy also does not change
D) All of the above E) None of the above