Energy and Simple Harmonic Motion

A pendulum is released from point A and oscillates as shown. Assume there is no air resistance or friction. At which of the following positions is the potential energy equal to the total energy?

• A

• B

• C

• Not enough information

Answer explanation

At position C, the pendulum is at its highest point, where all the energy is potential energy. At this point, the potential energy equals the total energy, as kinetic energy is zero. Thus, C is the correct choice.

Use the PhET pendulum lab simulation to test the following scenario. We do not know the values of the mass or the initial displacement. Assume friction is 0.

A pendulum is 0.75 meters long and has a period of 4.17 seconds. The pendulum is on an unknown planet.  What is the gravity of the unknown planet?

• 9.8

• 3.4

• 1.7

• Greater than 9.8

Answer explanation

The formula for the period of a pendulum is T = 2π√(L/g). Rearranging gives g = 4π²L/T². Plugging in L = 0.75 m and T = 4.17 s results in g ≈ 1.7 m/s², confirming the correct answer is 1.7.

The period of a pendulum is the time required for one complete cycle, for example, a left swing and a right swing. The period of a pendulum may be decreased by. . .

• Increasing the mass of the bob

• moving the equilibrium point

• decreasing the mass of the bob

• shortening the length of pendulum

Answer explanation

The period of a pendulum is determined by its length. Shortening the length of the pendulum decreases the period, allowing it to swing faster. Increasing or decreasing the mass does not affect the period.

The graph shows the variation with time of the displacement of an object undergoing simple harmonic motion. At which of the following time values is kinetic energy zero?

• 0 ms

• 40 ms

• 80 ms

• 100 ms

Answer explanation

In simple harmonic motion, kinetic energy is zero at the maximum displacement (amplitude). The graph shows that at 40 ms, the object is at its maximum displacement, making kinetic energy zero.

An object oscillating in simple harmonic motion has a time period T. The first graph shows how its displacement varies with time. Which of the subsequent graphs, A to D, show how the kinetic energy, Ek, of the object varies with time? 

• A

• B

• C

• D

Answer explanation

In simple harmonic motion, kinetic energy varies with the square of the velocity, which is maximum when displacement is zero. Graph C shows a sinusoidal pattern that matches this behavior, indicating the correct variation of kinetic energy with time.