What is the amplitude of the resulting oscillations?

[yecko]

Homework Statement

A mass of 2.0 kg hangs from a spring with a force constant of 50 N/m. An oscillating force F = (4.8 N) cos[(3.0 rad/s)t] is applied to the mass. What is the amplitude of the resulting oscillations? Neglect damping. Answer: 0.15 m

Homework Equations

F=kx , the mass only change the equilibrium position, amplitude is when max F thus cos is equal to 1

The Attempt at a Solution

F=4.8N, k=50N/m
x=F/k
=4.8/50
=0.096m.

What's wrong with my calculation? Thanks

 

[ehild]

Homework Statement

A mass of 2.0 kg hangs from a spring with a force constant of 50 N/m. An oscillating force F = (4.8 N) cos[(3.0 rad/s)t] is applied to the mass. What is the amplitude of the resulting oscillations? Neglect damping. Answer: 0.15 m

Homework Equations

F=kx , the mass only change the equilibrium position, amplitude is when max F thus cos is equal to 1

The Attempt at a Solution

F=4.8N, k=50N/m
x=F/k
=4.8/50
=0.096m.

What's wrong with my calculation? Thanks

The mass experiences three forces, gravity, mg, spring force, (-kx) and the driving force F. Gravity changes the equilibrium position only, but F is not equal to kx.

 

[yecko]

the mass only change the equilibrium position

Yes, I understand and i have mentioned it in the first post

F is not equal to kx.

So what to calculate?
Thanks

 

[ehild]

Yes, I have mentioned it

So what to calculate?
Thanks

The amplitude of vibration.

 

[yecko]

The amplitude of vibration.

I know, frankly its the question~
i mean how i can calculate in order to get the amplitude of vibration (the answer!)
what are the formulae to be used and the steps for getting the answer, if my steps are wrong (whats wrong?? why F is not equal to k*dx ?)
thanks

(ps. what I mentioned in the first posts are things all i understand... please tell me what i have misunderstood...)

 

[Lavar]

Really wish I could help you here, but no matter how I look at this question I get the same answer you do, and the only answer I can find online is formatting that makes no sense;

- A = ( F m ) ( 2 2 ) 2 ( b 2 m ) 2 = ( 4.8 N 2 kg ) [ ( 3 s 1 ) 2 ( 50 N m 2 kg ) ] 2 + = 0.15 m -

I'd keep trying but its like 2 am, hope somebody else helps you find your answer.

 

[yecko]

well, indeed the format goes wrong by directly copy and paste would make it unreadable

it seems we are on the another half of the planet:) it is still early here~
however i am going to have exam tomorrow, hope all problems in my exercises can be settled by today:)
thank you very much

 

[ehild]

Can you write Newton's second law for this object? Remember, you have to take two forces into account.
The object does SHM -simple harmonic motion. What is its displacement x in terms of time?
You certainly learned about driven oscillation. The object will oscillate with the frequency of the diving force after some time. What is the angular frequency of the external force?
See the x(t) function of the forced oscillator in http://www.physics.louisville.edu/cldavis/phys298/notes/resonance.html, with the damping b neglected.

 

[yecko]

Can you write Newton's second law for this object?

F=ma

What is its displacement x in terms of time?

x=A cos(ωt+Θ)

What is the angular frequency of the external force?

F = (4.8 N) cos[(3.0 rad/s)t]

ω=3

 

[ehild]

F=ma

F = ma is valid if F means the net force applied to the object. What is that net force in this case?

x=A cos(ωt+Θ)ω=3

The driving force is F_D=4.8 cos(3t) . The elastic force is Fe=-kx. What is the net force?
If what you said F_D=kx, the net force is zero, and the acceleration is zero. The object can not oscillate.

 

[yecko]

What is the net force?

Fd+Fe?

FD=kx, the net force is zero

Why? I mean when the spring length is amplitude, force is max, accerleration is max.

 

[ehild]

Fd+Fe?

Yes, and what is in terms of time and x?

Why? I mean when the spring length is amplitude, force is max, accerleration is max.

You speak about the spring force. But there are two forces, applied on the object, and the acceleration is (Fd+Fe)/m.

 

[yecko]

Yes, and what is in terms of time and x?

Fd=4.8 cos(3t) , Fe=-kx
F(net)=4.8 cos(3t) +-kx

Gravity changes the equilibrium position only

acceleration is (Fd+Fe)/m

are they contradict?

 

[ehild]

Fd=4.8 cos(3t) , Fe=-kx
F(net)=4.8 cos(3t) -kx

Yes. So ma=4.8 cos(3t) -kx. And the object performs SHM, with the frequency of the driving force, so x=Bcos(3t+θ). What is the acceleration then?

 

[yecko]

nothing

 

[yecko]

nothing

 

[ehild]

x=Acos(3t+θ) [A=amplitude?]
a=-9Acos(3t+θ)

yes. And ma=4.8cos(3t)-kx. What should be A and θ?

 

[yecko]

A = 0.096(?) and θ=0
step:50Acos(3t+θ)=4.8cos(3t)
whats wrong with my calculation?

 

[ehild]

A = 0.096(?) and θ=0
step:50Acos(3t+θ)=4.8cos(3t)
whats wrong with my calculation?

How did you get the equation 50Acos(3t+θ)=4.8cos(3t)? You think that the acceleration is zero? That is wrong.

 

[yecko]

substitute a and x into ma=4.8cos(3t)-kx

 

[ehild]

substitute a and x into ma=4.8cos(3t)-kx

Where is a?

 

[yecko]

oh
i got it
i mixed up the plus and minus sign only
thank you very much for your help!