Question

harmonic if the period (the time for one cycle) does not depend on the amplitude (the maximum displacement from equilibrium). In the following set, identify the oscillations that are simple harmonic, the ones that are approximately simple harmonic, and the ones that are not simple harmonic. Please comment on why/how you make your identifications.

1. The pendulum in a grandfather clock

2. A boat in water pushed down and released

3. A child on a swing

4. A mass hanging from a spring

5. A ping pong ball bouncing on the floor.

Answer 1

1)The pendulum in a grandfather clock - The classic example of simple harmonic motion. The bob moves back and forth exactly in a very steady manner and the following equation is applicable for time calculation:

T = 2 pi sqrt (L/g)

which proves that the period is independent of amplitude.

2) A boat in water pushed down and released - Not an example of SHM. In this case, Buoyant force will be in picture and the boat will be pushed back by the water as a reaction.

3) A child on a swing -an example of SHM. The child will swing back and forth and the period will be independent of amplitude in this case and can be calculated by the same formula in part 1.

4)A mass hanging from a spring - Also a classic example of SHM. The mass will oscillate with the period given by:

T = 2 pi sqrt (m / k)

where, m is the mass and k is the spring constant.

we see that the period is independent of amplitude of the oscillations.

5)A ping pong ball bouncing on the floor - Not an example of SHM. As its acceleration would keep on decreasing with time.