Simple Harmonic Motion Self Test

A. $10 \;cm$ - Correct!
B. $20 \;cm$ - No. That is the total displacement.
C. $31\; cm$ - No.
D. $40 \;cm$ - No.
E. $62 \;cm$ - No.

A. $0.00 \pi \; \mathrm {rad} \;s^{-1}$ - No. If the speed is given by $v(t) = -\omega A \sin(\omega t)$ what is its maximum value?
B. $0.25 \pi \; \mathrm {rad} \;s^{-1}$ - No. If the speed is given by $v(t) = -\omega A \sin(\omega t)$ what is its maximum value?
C. $0.50 \pi \; \mathrm {rad} \;s^{-1}$  - No. If the speed is given by $v(t) = -\omega A \sin(\omega t)$ what is its maximum value?
D. $0.75 \pi \; \mathrm {rad} \;s^{-1}$  - No. If the speed is given by $v(t) = -\omega A \sin(\omega t)$ what is its maximum value?
E. $1.0 \pi \; \mathrm {rad} \;s^{-1}$ - Correct!

$v = -\omega A \sin \omega t$

Maximum value when $\sin = 1$

$|v_{max}| = \omega A$

$\omega = |v_{max}|/A = 31/10 = 3.1 = 1.0 \pi \; s^{-1}$

A. $0.25 s$ - No. It hasnt gone through a full cycle.
B. $0.5 s$ - No. It hasnt gone through a full cycle.
C. $0.75 s$ - No. It hasnt gone through a full cycle.
D. $1.0 s$ - Correct!
E. $2.0 s$ - No. It has gone more than one full oscillation.

A. $0.00 \pi \; rad \; s^{-1}$ - No that is not correct. What is the relationship between $\omega$ and $T$?
B. $0.50 \pi \; rad \; s^{-1}$ - No that is not correct. What is the relationship between $\omega$ and $T$?
C. $1.0 \pi \; rad \; s^{-1}$ - No that is not correct. What is the relationship between $\omega$ and $T$?
D. $1.5 \pi \; rad \; s^{-1}$ - No that is not correct. What is the relationship between $\omega$ and $T$?
E. $2.0 \pi \; rad \; s^{-1}$ - Correct!

$\omega = 2\pi /T = 2 \pi/1 = 2\pi \;s^{-1}$ 

A. $15.0\; cm$ - Correct!
B. $23.0 \;cm$ - No. What is the expression for the maximum velocity?
C. $94.0 \;cm$ - No. What is the expression for the maximum velocity?
D. $156 \;cm$ - No. What is the expression for the maximum velocity?
E. $188 \;cm$ - No. What is the expression for the maximum velocity?

$v_{max} = -\omega A$
$A =  v_{max}/\omega = 94/2\pi = 15 \; \mathrm cm$

A. $5.0 \;cm$ - No. That is not correct. What are the expressions for the velocity and the maximum velocity?
B. $10\; cm$ - Correct!
C. $15 \;cm$ - No. That is not correct. What are the expressions for the velocity and the maximum velocity?
D. $20 \;cm$ - No. That is not correct. What are the expressions for the velocity and the maximum velocity?
E. $25 \;cm$ - No. That is not correct. What are the expressions for the velocity and the maximum velocity?

$v = -\omega A \sin \omega t$
$v_{max} = -\omega A = 47$

$v = 47 \sin \omega t$

$23.5 = 47 \sin \omega t$
$\sin \omega t = 1/2$
$\omega t = 30^ \circ$

$x = A \cos \omega t$
$8.7 = A \cos 30 = 0.866$

$A = 8.7/0.866 = 10 \mathrm {cm}$

A. $0.00 \pi \; rad \; s^{-1}$ - No. What is the relation for $v_{max}$?
B. $0.50 \pi \; rad \; s^{-1}$ - Correct!
C. $1.0 \pi \; rad \; s^{-1}$ - No. What is the relation for $v_{max}$?
D. $1.5 \pi \; rad \; s^{-1}$ - No. What is the relation for $v_{max}$?
E. $2.0 \pi \; rad \; s^{-1}$ - No. What is the relation for $v_{max}$?

$v_{max} = -\omega A$

but $A = 10$

$\omega = 47/10 = 0.75 (2\pi)$