THE UNIVERSITY OF BRITISH COLUMBIA
Science 1
Physics Assignment # 1:
WAVES
05 Jan. 2000 - finish by 12 Jan. 2000
- 1.
- DHM Review:
A mass m is attached to a spring with force constant k
and set in motion. The amplitude of the resulting oscillation is xm.
At a certain instant (which we will call t=0)
when the displacement from equilibrium
is exactly half the amplitude, (
),
a damping force
,
(where v
is the velocity of the mass) begins to act.
One second later the velocity is zero, the acceleration is
a[t=1 s] = 8 cm/s2
and the position is x[t=1 s] = -2 cm.
Another second later the position is x[t=2 s] = 0.5 cm.
Find the initial phase ,
the angular frequency ,
the damping coefficient
and
the initial amplitude xm.
(Warning: The approximation
is only accurate to 13%!)
- 2.
- Travelling Wave in a String:
We are observing a string whose transverse displacement y
is given [in
units] as a function of time t
and position z (down the length of the string) by
- (a)
- In what direction is the wave traveling?
- (b)
- What is the amplitude of the traveling wave?
- (c)
- What is the frequency of
at any point on the string?
- (d)
- What is the wave propagation velocity on the string?
Also try the following problems from Tipler Ch. 13:
6, 7
Jess H. Brewer
2000-01-05