SHM, The Doppler Effect, Interference, Single Slit Diffraction, Resolution

A 4kg mass oscillates on a spring as shown, performing simple harmonic motion (SHM). The amplitude of oscillation is 10cm, and the angular velocity is 5 rad s^{1} .
Oleg Alexandrov http://commons.wikimedia.org/ 

1. The potential energy due to SHM at the centre of oscillation is
 A. 0 J
 B. 0.5 J
 C. 1 J
 D. 5 KJ


2. The total energy of the system is
 A. 5 J
 B. 0.5 J
 C. 1 J
 D. 5 KJ


3. The maximum velocity is
 A. 0.5 ms^{1}
 B. 5 ms^{1}
 C. 50 ms^{1}
 D. 500 ms^{1}


4. The time period of the spring shown above is measured to be T.
If the spring is replaced with one where the spring constant k is 4 times larger, and the mass is reduced to 1kg, the new time period will be
 A. 4T
 B. 2T
 C. T/2
 D. T/4


5. A pendulum in a clock performs SHM as it oscillates with amplitude 0.2m. The time taken for an oscillation is exactly 2s. The value of ω (angular velocity) and f (frequency) are therefore

ω (rad s^{1}) 
f (Hz) 
A 
π 
0.5 
B 
π 
π 
C 
4 π 
0.5 
D 
4 π 
π 



6. A police car is moving towards an observer with its siren switched on. Compared to the source, the sound as measured by the observer will have
 A. a higher frequency and higher velocity
 B. a lower frequency and a higher velocity
 C. a higher frequency and the same velocity
 D. a lower frequency and the same velocity


7. A galaxy is moving away from Earth at 1% the speed of light. Radio waves of original frequency 10^{6 }Hz will be observed to have a frequency of
 A. 1.1 x 10^{6 }Hz
 B. 1.01 x 10^{6 }Hz
 C. 9.9 x 10^{5 }Hz
 D. 9.99 x 10^{5 }Hz



8. The Doppler effect can be used to find the velocity of a source. Whcih of the following statements gives the application AND correctly states the wave that can be used ?
I 
Speed cameras on roads, using radio waves 
II 
Blood flow rates, using ultrasound 
III 
Speed of galaxy recession, using visible light 
 A) I only
 B) I and II only
 C) II and III only
 D) All 3 statements



