Quiz 1 for PHYS262, Summer 2001

July 18, 2001

1

A particle's displacement is given as a function of time by

$$x(t) = A\cos\omega t + B \sin \omega t~.$$

What is the correct velocity $v(t)$ and acceleration $a(t)$ ?

(a)

$v(t) =-\omega ^2 A\cos\omega t -\omega^2 B \sin \omega t$, $a(t) = -\omega A\sin \omega t +\omega B \cos \omega t$

(b)

$v(t) = \omega A\sin \omega t +\omega B \cos \omega t$, $a(t) =\omega ^2 A\cos\omega t +\omega^2 B \sin \omega t$

(c)

$v(t) = -\omega A\sin \omega t +\omega B \cos \omega t$, $a(t) =-\omega ^2 A\cos\omega t -\omega^2 B \sin \omega t$

(d)

$v(t) = \omega A\sin \omega t -\omega B \cos \omega t$, $a(t) =-\omega ^2 A\cos\omega t -\omega^2 B \sin \omega t$

(e)

None of the above

2

In Problem 1, what is the period of oscillation?

(a) $\omega$ (b) $1\over\omega$ (c) $2\pi\over \omega$ (d) $\omega \over 2\pi$ (e) $1 \over 2\pi \omega$

3

See Fig. . In the figure is displayed the displacement of a particle with mass $m$ as a function of time undergoing a simple harmonic oscillation attached to a spring. At $t=t_0$, by collision with another particle, it suddenly changes its mass and continues its oscillation with the same spring. What is the new mass of the particle after time $t_0$?

Figure: Prob 3

(a) $m/2$ (b) $m/4$ (c) $2m$ (d) $4m$ (e) None of the above

4

The period of a simple pendulum shown in Fig. is $T$. How do you double the period of oscillation?

Figure: Prob 4

(a)

Change the length of the pendulum to $2L$.

(b)

Double the thickness of the string.

(c)

Change the mass to $m/4$.

(d)

Change the mass to $4m$.

(e)

None of the above.