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Stewart_Calc_7ET ch17sec03
MULTIPLE CHOICE
1. A spring with a -kg mass has natural length m and is maintained stretched to a length
of m by a force of N. If the spring is compressed to a length of m and then
released with zero velocity, find the position of the mass at any time .
a.
b.
c.
d.
e.
2. A spring has a mass of kg and its damping constant is . The spring starts from its
equilibrium position with a velocity of m/s. Graph the position function for the spring
constant .
a.
c.
b.
3. A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30
N. If the spring begins at its equilibrium position but a push gives it an initial velocity of
m/s, find the position x(t) of the mass after t seconds.
a.
b.
c.
d.
e.
4. A spring with a mass of kg has damping constant 28 and spring constant . Find the
damping constant that would produce critical damping.
a.
b.
c.
d.
9
e.
5. A series circuit consists of a resistor , an inductor with , a capacitor with
, and a -V battery. If the initial charge is 0.0008 C and the initial current
is 0, find the current I(t) at time t.
a.
b.
36 195
2340
6 195
c.
d.
e.
6. The figure shows a pendulum with length L and the angle from the vertical to the
pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential
equation where
we can use the linear approximation
a.
b.
c.
d.
e.
7. A series circuit consists of a resistor , an inductor with , a capacitor with
, and a generator producing a voltage of If the initial
charge is and the initial current is 0, find the charge at time t.
a.
b.
c.
d.
e.
8. A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the
position function of the mass at time t if it starts at the equilibrium position with a velocity
of 2 m/s.
a.
c.
b.
9. Suppose a spring has mass M and spring constant k and let . Suppose that the
damping constant is so small that the damping force is negligible. If an external force
is applied (the applied frequency equals the natural frequency), use the
method of undetermined coefficients to find the equation that describes the motion of the
mass.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. A spring with a mass of 2 kg has damping constant 14, and a force of N is required to
keep the spring stretched m beyond its natural length. Find the mass that would produce
critical damping.
2. A series circuit consists of a resistor an inductor with L = H, a capacitor with
C = F, and a -V battery. If the initial charge and current are both 0, find the
charge Q(t) at time t.
3. A spring with a mass of 2 kg has damping constant 14, and a force of N is required to
keep the spring stretched m beyond its natural length. The spring is stretched 1m
beyond its natural length and then released with zero velocity. Find the position x(t) of the
mass at any time t.
