Question

. For small amplitudes of oscillation the motion of a pendulum is simple harmonic. For a pendulum with a period of , find the ground-level energy and the energy difference between adjacent energy levels. Express your results in joules and in electron volts. Are these values detectable?

Short answer

The ground level energy and the energy difference between the adjacent energy levels

The energy difference between the adjacent energy levels

These energies are extremely small to be detected by current technology.

Step-by-step solution

About Simple harmonic motion

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position.

Determine the ground level energy and the energy difference between the adjacent energy levels

From equation 40.46, the energy levels for the harmonic: oscillator are given by :

From equation 142, the angular frequency is related to the period by the relation:

Step 2

Givens

The period of the pendulum is T = 0.500s -

Step 3 3 C

Calculations

First, We plug our value for T in equation (2), so we get the angular frequency of this pendulum:

The ground level corresponds to n = 0; Thus, We plug our values for n and to into equation (I), so we get the ground-level

energy of the pendulum:

therefore the ground level energy and the energy difference between the adjecent energy levels

From equation (1), we get the difference in energy between two adjacent levels En and En+1 as follows;

50, We plug our value for E0, so We get the energy separation betWeen two adjacent levels:

Therefore the the energy difference between the adjacent energy levels

These energies are extremely small to be detected by current technology.