CHAPTER 9 SIMPLE HARMONIC MOTION AND HOOKE’S LAW H QUESTIONS AND ANSWERS
6. Calculate the length of a simple pendulum that has a period of 2.8 s.
Solution T = 2π
__ √
__ l g ⇒ 2.8 = 2π
____ √
_____ l 9.8
You may now complete Exercise 9C. CHAPTER 9 EXERCISE 9A
1. An elastic system that obeys Hooke’s law has an elastic constant k of 2500 N m−1.
(i) Calculate its displacement when a force of 200 N is exerted.
(ii) Calculate its restoring force when a displacement of 10 cm is made.
CHAPTER 9 EXERCISE 9B
1. Explain why the motion of a ball bouncing off the ground is not representative of SHM.
2. A mass undergoes SHM with 30 complete cycles in 60 seconds. Calculate its frequency and period.
3. If a pendulum oscillates 5 times in 40 seconds, what is the frequency and period of this system?
4. A particle undergoing SHM is accelerating at 3 m s−2 when displaced by 20 cm. Calculate its frequency.
5. If a 5 kg mass undergoing SHM has a frequency of oscillation of 2 Hz, calculate the resultant force on it when its displacement from equilibrium is: (i) 5 cm
(ii) 3 cm
6. If the period of a system exhibiting SHM is 4 seconds, calculate the acceleration when it is displaced 20 cm from equilibrium.
7. A 10 kg particle experiences maximum amplitude when a 100 N force acts on it. Calculate the particle’s amplitude if its acceleration is 6 m s−2 when it is displaced by 0.2 m.
CHAPTER 9 EXERCISE 9C g = 9.81 m s−2
1. A pendulum clock on Earth is accurate in timing a minute. If the same clock were brought to the Moon, what time would it register in an actual minute? (Moon’s
gravity = 1
__ 6 g)
2. If a spring is stretched 15 cm beyond its rest point, the restoring force generated is 10 N.
(i) Calculate the displacement undergone when the restoring force is 20 N.
(ii) Calculate the restoring force generated when the displacement is 10 cm.
Square both sides: 7.84 = 4π2
( l _____ 9.8
) ⇒ l = (7.84)(9.8) ______________
4π2 = 1.946 m
2. Calculate the length of a simple pendulum that has a period of 3 s.
3. If a simple pendulum has a string length of 2.2 m and undergoes 40 cycles in 1 minute, calculate gravity at this point.
