SIMPLE HARMONIC MOTION



SIMPLE HARMONIC MOTION

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1. A coiled spring is stretched 0.50 m by a mass weighing 0.50 N that is hung from one end. How far will it be stretched by a mass weighing 1.00 N?

2. The hook of a spring balance is pulled down 5.00 cm by a mass weighing 40.0 N (a) If a mass weighing 125.0 N is substituted for the previous mass, how far is the hook pulled down? (b) If the balance is precise to the nearest 5 N, how far apart are the 5.00 N graduations?

3. A 5 kg body is suspended by a long and light spiral spring. An added force of 2 N stretches the spring an additional 25 cm. Find the force constant of the spring.

4. A coiled spring is stretched 8 cm by a load of 0.5 N Find the force constant of the spring.

5. A piece cut from a bicycle inner tube is 0.7 m long when it carries a load of 25 N. The force constant k is 300 N/m. What will be the length of a piece of rubber when the load is 75 N?

6. A spring makes 12 vibrations in 3 seconds. Find (a) the period and (b) the frequency of the vibration.

7. A vibrating reed in a harmonica makes 200 vib/sec. What is the period?

8. What is the time required for 2400 vibrations of a loaded spring if the frequency is 4 vib/sec?

9. The piston of an engine moves a total distance of 0.2 m from one extreme point to the other. (a) What is the amplitude? (b) What is the displacement when the piston is 0.1 m from one end of its stroke?

10. The piston of problem 9 makes 2 vib/sec. How fast is it moving when passing through the midpoint of its path?

11. Compute the time for one vibration of a spring whose force constant is 16 N/m, if the load has a mass of 1 kg.

12. A point on a horizontal vibrating piano string is moving up and down in SHM with a frequency of 200 vib/sec. The maximum displacement of the point below its normal position is 0.5 mm. (a) What is the maximum velocity of the particle, and where is the velocity reached? (b) What is the maximum acceleration of the particle?

13. A coiled spring is stretched 8 cm by a load of 0.5 N. A 2 N body is then attached to the spring and set into vibration with an amplitude of 120 cm. Find the maximum restoring force acting on the vibrating body.

14. A 30 g load hangs from a long, light spring. When pulled down 20 cm below its equilibrium position and released, it vibrates with a period of 2 s. (b) By how much will the spring shorten if the load is removed?

15. A raft of weight 4000 N is floating in a pond. When a 1000 N man climbs on board, the raft sinks 0.04 m deeper into the water to a new equilibrium position. If the man jumps off, how many vertical vibrations does the empty raft make in 5 s?

16. A load of mass 400 g is hanging from a light spring whose force constant is 10 N/m. The load is pulled down 10 cm from its equilibrium position and released. (a) How long does it take for the load to reach the equilibrium position again? (b) What is its velocity then?

17. An object that weights 25 N is moving with SHM of frequency 60 vib/min and amplitude 1.5 m. What is the restoring force when the object is at one of the end points?

18. A light rubber band is hanging loosely from the ceiling. A load is attached to the free end of the rubber band, and it is observed that the load, when released, moves downward a distance of 40 cm before starting to rise again. What is the period of this SHM?

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19. Compute the length of a clock pendulum that ticks once each second. (Hint: It ticks twice during each complete vibration).

20. What would be the period of a pendulum suspended from the top of a tall building on a light string 353 m long?

21. The value of the acceleration due to gravity on the moon is about 1/6 that on the earth. What would be the period on the moon of a simple pendulum whose period on the earth is 2.0 s?

22. A pendulum 0.25 m long has a period of 1.1 s. What is the period of a pendulum in the same location if it has a length of 0.l0 m?

23. What is the period of a pendulum 1.5 m long at sea level?

24. What is the value of g for a location where a pendulum 1.08 m long has period of 2.05 s?

25. A seconds pendulum is one with a period of exactly two seconds. Find the length of a seconds pendulum of Denver, Colorado (g = 9.79609 m/s2).

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