Damped Simple Harmonic Motion problem

In summary: Find the natural logarithm of 0.65. Then you can find the damping constant b.In summary, the conversation discusses the process of estimating the values of the spring constant k and damping constant b for a suspension system based on the sag and oscillation amplitude of a car. The approach involves using Hooke's law and finding the period and natural logarithm to calculate the constants.
  • #1
davegillmour
9
0
I'm having trouble with this problem.The suspension system of a 2100 kg automobile "sags" 7.2 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 35% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 525 kg.
 
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  • #2
a) I know that k=mw^2 but don't know where I can get w from.

b)Xe^(-bt/2m)= .65X which breaks down to b=(-2m*ln(.65))/t but I don't know how/if I can't get a t.

Is there something I'm not seeing or am I totally off in my approach?

Any help is appriciated
 
  • #3
davegillmour said:
a) I know that k=mw^2 but don't know where I can get w from.
You can't get omega. The way to do it is to use Hooke's law. You know the distance by which the springs get compressed when the chassis is laid down. The force exerted by the spring at the new equilibrium position must cancel the force exerted by gravity. That will give you k.
b)Xe^(-bt/2m)= .65X which breaks down to b=(-2m*ln(.65))/t but I don't know how/if I can't get a t.

Is there something I'm not seeing or am I totally off in my approach?

Any help is appriciated

The time wil correspond to one period (since it`s after one cycle). Knowing k and m you can find the period.
 

What is damped simple harmonic motion?

Damped simple harmonic motion is a type of oscillatory motion in which the amplitude of the oscillations decreases over time due to the presence of an external damping force.

What factors affect the rate of damping in a damped simple harmonic motion?

The rate of damping in a damped simple harmonic motion is affected by the magnitude of the damping force and the properties of the oscillating system, such as mass, spring constant, and initial amplitude of the motion.

How is the damping coefficient calculated in a damped simple harmonic motion?

The damping coefficient in a damped simple harmonic motion is typically calculated by dividing the damping force by the velocity of the oscillating object at a specific point in time.

What is the equation for damped simple harmonic motion?

The equation for damped simple harmonic motion is x = A * e^(-bt) * cos(ωt + φ), where x is the displacement of the oscillating object, A is the initial amplitude, b is the damping coefficient, t is time, ω is the angular frequency, and φ is the phase angle.

How does the presence of damping affect the period and frequency of a damped simple harmonic motion?

The presence of damping increases the period and decreases the frequency of a damped simple harmonic motion compared to an undamped simple harmonic motion. This is because the damping force reduces the amplitude of the oscillations, causing the object to take longer to complete each cycle and have a lower frequency.

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