# Lightly Damped Simple Harmonic Oscillator

• DrDank
In summary, a tuning fork with a natural frequency of 392Hz and an angular frequency of 2463 (rad/s) has a damping factor of approximately 0.23, as calculated by using the equation A(t) = A_{o} e^{-t\gamma} and given information about the amplitude after 10 seconds.
DrDank
Tuning forks are lightly damped SHO's. Consider a tuning fork who's natural frequency is f=392Hz. Angular frequency = w = 2(Pi)f = 2463 (rad/s)

The damping of this tuning fork is such that, after 10 sec, it's amplitude is 10% of it's original amplitude.

Here is my attempt to find the damping factor (gamma)
Amplitude as a function of time where g is the damping factor (g = gamma)$$A(t) = A_{o} e^{-t\gamma}$$

$$A(10) = \frac{1}{10} A(0)$$

$$A_{o}e^{-10\gamma} = \frac{1}{10} A_{o} e^{0}$$

$$e^{-10\gamma} = \frac{1}{10}$$

$$-10 \gamma = \ln{\frac{1}{10}}$$

$$\gamma = \frac{\ln{10}}{10} = .23$$

Is this right?

Last edited:
You can check your result yourself by substituting it back into the original equation.

## 1. What is a lightly damped simple harmonic oscillator?

A lightly damped simple harmonic oscillator is a system that experiences oscillatory motion due to a restoring force that is proportional to its displacement from equilibrium, and also experiences a small amount of damping that causes its amplitude to decrease over time.

## 2. What causes damping in a simple harmonic oscillator?

Damping in a simple harmonic oscillator can be caused by various factors, such as air resistance, friction, or energy dissipation through heat.

## 3. How does damping affect the motion of a simple harmonic oscillator?

Damping causes the amplitude of the motion in a simple harmonic oscillator to decrease over time, resulting in a decrease in the frequency and period of the oscillations.

## 4. What is the equation for a lightly damped simple harmonic oscillator?

The equation for a lightly damped simple harmonic oscillator is x(t) = Ae-btcos(ωt + φ), where x(t) is the displacement from equilibrium at time t, A is the amplitude, b is the damping constant, ω is the angular frequency, and φ is the phase angle.

## 5. How does the damping constant affect the motion of a simple harmonic oscillator?

The damping constant affects the rate at which the amplitude of the motion decreases. A larger damping constant results in a faster decrease in amplitude, while a smaller damping constant leads to a slower decrease in amplitude.

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