# Damped Simple Harmonic Motion: Finding Amplitude Reduction in Carbon Dioxide

• erisedk
In summary, the amplitude of a simple pendulum oscillating in air with a small spherical bob decreases from 10 cm to 8 cm in 40 seconds. Using Stokes Law and the ratio of the coefficient of viscosity of air to that of carbon dioxide, the time for the amplitude to decrease from 10 cm to 5 cm in carbon dioxide is close to (ln 5 = 1.601, ln 2 = 0.693). By dividing equation 1 by equation 2 and solving for the unknown variables, the time can be determined.
erisedk

## Homework Statement

The amplitude of a simple pendulum oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes Law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide will be close to (ln 5 = 1.601, ln 2 = 0.693)

## Homework Equations

x(t) = Ae-bt/2m cos(ωt + Φ)

## The Attempt at a Solution

I suppose that b ∝ viscosity
So, assuming b/2m = k
8 = 10e-k×40 ------- (1)
5 = 10e-k×t/1.3 ---------- (2)
Dividing 1/2 --
8/5 = ekt/1.3 - 40k

I have no idea what to do beyond this, I haven't been given values for b or m. Also, my solution may be very wrong because I'm not sure about this at all.

why did you divide [1] by [2]?

Oh my god, this is embarrassing. Got it, two equations, two unknowns. Thank you :D

using equation 1 , find k value and put that in equation 2 to find the value of time

## 1. What is damped simple harmonic motion?

Damped simple harmonic motion is a type of motion in which a system experiences a restoring force that is proportional to its displacement from its equilibrium position, but also experiences a damping force that decreases its motion over time.

## 2. What causes damped simple harmonic motion?

Damped simple harmonic motion is caused by the presence of a damping force in a system, which can be due to factors such as friction, air resistance, or energy loss through other mechanisms.

## 3. How is damped simple harmonic motion different from regular simple harmonic motion?

The main difference between damped simple harmonic motion and regular simple harmonic motion is the presence of a damping force. In regular simple harmonic motion, the system would continue to oscillate indefinitely, whereas in damped simple harmonic motion, the damping force causes the motion to decrease over time.

## 4. How is the amplitude of damped simple harmonic motion affected?

In damped simple harmonic motion, the amplitude decreases over time due to the presence of the damping force. This means that the oscillations become smaller and smaller until they eventually stop.

## 5. Is damped simple harmonic motion a real-life phenomenon?

Yes, damped simple harmonic motion is a real-life phenomenon that can be observed in many systems. For example, a swinging pendulum will eventually come to a stop due to air resistance and friction, which are forms of damping forces. Other examples include the vibrations of a guitar string or the motion of a car's suspension system.

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