# Oscillation/amplitude question

• unhip_crayon
In summary, the amplitude of the oscillations is 116 cm, and the angular frequency is 2.8 Hz. The maximum acceleration is 16.0 rad/s2.
unhip_crayon
Heres the question I am having problems solving...

A 3.00kg block hangs from a spring with a spring constant of 200.N/m and is set into vertical oscillation. The block has a velocity of 0.900m/s upwards when the spring is stretched by 11.0 cm. Calculate the amplitude of the oscillation.

So here's what I got...

K=200
m=3.00
V=0.900
x=0.11m
Xm=?

solve for Xm using this equation

Am I doing it right?
Help ASAP
Thank You

Last edited by a moderator:
unhip_crayon said:
solve for Xm using this equation

Am I doing it right?
Help ASAP
Thank You

Yes, provided the stretch is measured from the equilibrium position in which the mass hangs after being put on the spring. In this problem, that seems to be implied.

Last edited by a moderator:
but the answer I am getting is incorrect. The correct answer is 11.6cm (yes i did convert m to cm from my final answer)

Thanks

unhip_crayon said:
A 300kg block hangs from a spring with a spring constant of 200.N/m and is set into vertical oscillation. The block has a velocity of 0.900m/s upwards when the spring is stretched by 11.0 cm. Calculate the amplitude of the oscillation.

So here's what I got...

K=200
m=3.00
V=0.900
x=0.11m
Xm=?

It may help to note that you have somehow transmuted 300 kg into 3 kg!

Using the correct mass, the amplitude of the oscillation is 1.16 m or 116 cm - which is what is was supposed to be apart from a factor of 10? Did you mess up the decimals here as well? (No hard feelings, that happens for the best of us)

Troels said:
It may help to note that you have somehow transmuted 300 kg into 3 kg!

Using the correct mass, the amplitude of the oscillation is 1.16 m or 116 cm - which is what is was supposed to be apart from a factor of 10? Did you mess up the decimals here as well? (No hard feelings, that happens for the best of us)
Oops...sorry. It is suppose to be 3.00kg. According to the book, yes, the correct answer should be 11.6cm. Do you think you can solve it for me? I've got a midterm today at 11.30

Thanks

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unhip_crayon said:
Oops...sorry. It is suppose to be 3.00kg.

Are you sure it is not 300 *grams* = 0.3 kg? In that case I get 11.5 cm, which is the best so far - otherwise I get 15.6 cm

unhip_crayon said:
Do you think you can solve it for me?

The general symbolic solution is pretty obvious:

$$x_{\textrm{max}}=\sqrt{x^2+\frac{mv^2}{k}}$$
Which is also what you will get from a diffential-eq approach. So it is correct - It seems that you just need to get the numbers right.

Last edited:
Troels said:
Are you sure it is not 300 *grams* = 0.3 kg? In that case I get 11.5 cm, which is the best so far - otherwise I get 15.6 cm

The general symbolic solution is pretty obvious:

$$x_{\textrm{max}}=\sqrt{x^2+\frac{mv^2}{k}}$$
Which is also what you will get from a diffential-eq approach. So it is correct - It seems that you just need to get the numbers right.

ok...so maybe the books answer is incorrect because I got the same answer as you
Thanks

can I just check that this is the same sort of question?

"A mass at the end of a spring oscillates with a period of 2.8s. The mazimum displacement of the mass from its equilibrium position is 16cm.

a) what is the amplitude of the oscillations?
b) i) its angular frequency;
ii) its maxium acceleration.

## What is oscillation?

Oscillation is the repetitive back-and-forth motion of an object or system between two positions or states.

## What causes oscillation?

Oscillation is caused by a restoring force that tries to return the object or system to its equilibrium position. Examples of restoring forces include gravity, tension, and elasticity.

## What is amplitude?

Amplitude is the maximum displacement or distance from the equilibrium position to the peak of an oscillation. It is a measure of the strength or intensity of the oscillation.

## How is amplitude related to energy?

Amplitude is directly proportional to the energy of an oscillation. This means that the higher the amplitude, the more energy the oscillation has.

## How can the amplitude of an oscillation be changed?

The amplitude of an oscillation can be changed by adjusting the energy or force acting on the system, such as changing the initial conditions or introducing damping forces. It can also be changed by altering the properties of the system, such as its mass or stiffness.

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