The Importance of Damping in Simple Harmonic Motion Explained

[krissh]

I need help for the second part please. How do the oscillations being damped prevent them from being S.H.M. as well the other 2 points? I need an explanation so I can understand. The oscillations would still have the same time period eve if they are damped.

Low frequency due to mass/density (of spheres)

Can someone please explain that to me as I don't understand it.

Isn't T supposed to be constant as it is independent of the amplitude theta, right?

T=2π√(m/k)
So surely as m increases T increases like the graph of y=√x?

How does good suspension in a car help prevent resonance in the various parts of the car?
Prevention of resonance:
Damps oscillations (1)
Fewer forced oscillations (1)
Explanation of damping [e.g. in terms of energy transfers] (1) Max 2

For the last part, I understand that the suspension damps oscillations, but I'm not fully sure how there are fewer forced oscillations. Is it because that the damping causes the oscillations to die away quicker, so they stop quicker. Hence there are fewer forced oscillations?

I think the MS answer is wrong as I got k=1.40Nm^-1 using T=2π√(m/k). What did others get?


THANKS SO MUCH!

 

[Simon Bridge]

View attachment 65258
I need help for the second part please. How do the oscillations being damped prevent them from being S.H.M. as well the other 2 points? I need an explanation so I can understand. The oscillations would still have the same time period eve if they are damped.

What do the letters "S.H.M." stand for? Does this describe damped harmonic motion?

Low frequency due to mass/density (of spheres)
Can someone please explain that to me as I don't understand it.

How does the mass density affect the movement?

Isn't T supposed to be constant as it is independent of the amplitude theta, right?

Depends.

T=2π√(m/k)
So surely as m increases T increases like the graph of y=√x?

That equation makes some assumptions about the system - what if those assumptions do not hold?

How does good suspension in a car help prevent resonance in the various parts of the car?
Prevention of resonance:
Damps oscillations (1)
Fewer forced oscillations (1)
Explanation of damping [e.g. in terms of energy transfers] (1) Max 2

For the last part, I understand that the suspension damps oscillations, but I'm not fully sure how there are fewer forced oscillations. Is it because that the damping causes the oscillations to die away quicker, so they stop quicker. Hence there are fewer forced oscillations?

When the suspension is good - what do you want to happen to the oscillations?
Think about situations where you experience good suspension.

I think the MS answer is wrong as I got k=1.40Nm^-1 using T=2π√(m/k). What did others get?

Nope - that would amount to "doing the work for you", which is not allowed.
How did you get that answer? What was your reasoning?