# Q1: A mass-spring system is oscillating with amplitude A. The kinetic ```Phys101
Term:121
Online HW-Ch15-Lec02
Q1:
A mass-spring system is oscillating with amplitude A. The kinetic energy will equal
the potential energy only when the displacement is:
A. zero
B. &plusmn;A/2
C. &plusmn;A√2/2
D. &plusmn;A/4
E. anywhere between -A and +A
Ans:
𝐂; K = U
and ω2 =
⇒
1
1
mv 2 = kx 2 ⇒ m �ω2 A2 sin2 (ωt) = k�A2 cos2 (ωt)��
2
2
k
⇒ k = mω2 ; so sin2 (ωt) = cos2 (ωt)
m
tan2 (ωt) = 1 → tan(ωt) = &plusmn;1 ⇒ ωt = &plusmn;
∴ x = A cos( ωt) = &plusmn;A
Q2:
√2
2
π
4
Three physical pendulums of masses m 1 = m o , m 2 = 2m o , m 3 =3m o have the same
shape, size and are suspended at the same point. Rank the masses according to the
period of the pendulums, least first.
A.
B.
C.
D.
E.
1, then 2, then 3.
2, then 3, then 1.
3, then 1, then 2.
3, then 2, then 1.
All have the same period
Ans:
E, the mas will cancel out in the equation of the period of a physical pendulum
KFUPM-Physics Department
1
Phys101
Term:121
Online HW-Ch15-Lec02
Q3:
A meter stick is pivoted at one of its edges and is free to oscillate in a vertical plane
on a planet of unknown gravitational acceleration g. The meter stick is moved from
the equilibrium position by an angle of 15o and then released. Find the gravitational
acceleration (in m/s2) of the planet if the period of oscillation is measured to be 2 s.
Ans:
1 2
ML ; L = 1 meter
3
L
h = = 0.5
2
I=
T = 10 s;
I
4π2 &times; I
4π2 &times; ML2 /3
T = 2π�
⇒g= 2
=
Mgh
T Mh
T 2 Mh
⇒g=
4π2 &times; 1/3
= 6.58 m/s2
22 &times; 0.5
KFUPM-Physics Department
2
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