# PH 1140 WAVES and OSCILLATIONS

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```					PH 1140: WAVES and OSCILLATIONS                                             D2009

SAMPLE EXAM ONE

1. The point of the needle of a sewing machine moves in SHM along the x-axis with
frequency of 2.5 Hz. At t=0 s its position is +1.1 cm. At t=0 s its velocity component is
-15 cm/s. (a) Determine the angular frequency of the sewing machine needle. (b) What
is the phase of this motion (i.e. find φ). (c) Find the acceleration component of the needle
at t=0 s. (d) Write the equation of motion for the displacement of the sewing machine
needle, x(t). (e) Write the equation of motion for the velocity of the sewing machine
needle, v(t).

2. An unhappy rodent of mass 0.300 kg, moving on the end of a spring with force
constant k = 2.50 N/m, is acted on by a damping force Fx = - b vx. (a) If the constant b
has the value 0.900 kg/s, what is the frequency of oscillation of the rodent? (b) Write
down the equation of motion for the displacement of the rodent, x(t). (c) Write down the
equation of motion for the velocity of the rodent, v(t). (d) Write down the equation of
motion for the energy, E(t). (e) For what value of the constant b will the motion be
critically damped?

3. A certain alarm clock ticks four times each second, with each tick representing half a
period. The balance wheel consists of a thin rim with radius 0.55 cm, connected to the
balance staff by thin spokes of negligible mass. The total mass of the balance wheel is
0.90 g. (a) What is the moment of inertia of the balance wheel about its shaft? (b) What
is the torsion constant of the hairspring?

4. An L-R-C circuit has L=0.450 H, C=2.50 x 10-5 F, and resistance R. (a) What is the
angular frequency of the circuit when R = 0? (b) What is the value of the angular
frequency of the circuit when R = 100Ω ? (c) In terms of the given quantities and in
terms of the angular frequency corresponding to R = 100Ω, write down the equation
which describes how charge varies with time, q(t). (d) In terms of the given quantities
and in terms of the angular frequency corresponding to R = 100Ω, write down the
equation which describes how current varies with time, i(t). (e) In terms of the given
quantities and in terms of the angular frequency corresponding to R = 100Ω, write down
the equation which describes the energy stored within the inductor, as a function of time.

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