# Exploring b & n in Damped Harmonic Motion

• romd
In summary, b represents the y-intercept and n represents the gradient for the equation describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve.
romd

## Homework Statement

Concerning damped harmonic motion (mass on a spring using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what do b (y-intercept) and n (gradient) represent? (A=area of damper; T=time taken for amplitude to halve)

## Homework Equations

$$T=b.A^n$$
(i.e. $$ln(T)=n.ln(A) + ln(b)$$ )

The Attempt at a Solution b represents the time taken for the amplitude to halve when the area of the damper is equal to 1. n represents the rate at which the time taken for the amplitude to halve decreases as the area of the damper increases.

I would like to first clarify that the equation provided is not a standard equation for damped harmonic motion and may not accurately represent the behavior of the system. However, for the purpose of this question, let us assume that it is a suitable equation for the given scenario.

In this case, b and n represent the parameters of the equation, with b representing the y-intercept and n representing the gradient of the line on a logarithmic scale. The y-intercept, b, represents the value of T when A is equal to 1 (ln(A) = 0). This can be interpreted as the time taken for the amplitude to halve when there is no damper present (A=1).

On the other hand, the gradient, n, represents the rate of change between T and A on a logarithmic scale. A higher value of n would indicate a steeper slope, meaning that the time taken for the amplitude to halve decreases more rapidly as the damper size increases. This suggests that a larger damper has a greater effect on reducing the amplitude of oscillations.

It is important to note that the values of b and n may vary depending on the specific system and experimental conditions. Therefore, it is necessary to conduct further experiments and analyze the data to determine the most accurate values for these parameters.

## 1. What is damped harmonic motion?

Damped harmonic motion refers to the movement of an object in a system that experiences a resistive force, causing the amplitude of the oscillations to decrease over time.

## 2. How is damping represented in damped harmonic motion?

Damping is typically represented by a damping constant, which is a measure of how strong the resistive force is in the system. It is denoted by the symbol "b" in equations.

## 3. What is the equation for damped harmonic motion?

The equation for damped harmonic motion is x = A * e^(-bt/2m) * cos(ωt + φ), where x is the displacement, A is the initial amplitude, b is the damping constant, m is the mass of the object, ω is the angular frequency, and φ is the phase angle.

## 4. How does damping affect the motion of an object in damped harmonic motion?

Damping causes the amplitude of the oscillations to decrease over time, and it also affects the frequency and period of the motion. The higher the damping constant, the faster the amplitude will decrease and the longer the period will be.

## 5. What are some real-life examples of damped harmonic motion?

Some common examples of damped harmonic motion include a swinging pendulum that gradually slows down due to air resistance, a car's suspension system that absorbs vibrations from the road, and a guitar string that slowly loses its sound after being plucked due to internal friction.

• Introductory Physics Homework Help
Replies
5
Views
839
• Introductory Physics Homework Help
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
734
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
17
Views
375
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
14
Views
2K