# Oscillation Frequency, Total Mechanical Energy, and Initial Speed

• KatlynEdwards
In summary, the block on a frictionless surface is oscillated with an amplitude of 44 cm. The frequency is 1.0 Hz.
KatlynEdwards

## Homework Statement

The figure shows a block on a frictionless surface attached to a spring. The block is pulled out to position x_i = 20 cm, then given a "kick" so that it moves to the right with speed v_i. The block then oscillates with an amplitude of 44 cm.

Image of the problem - http://session.masteringphysics.com/problemAsset/1013861/11/jfk.Figure.Q14.21.jpg

What is the oscillation frequency?

What is the total mechanical energy of the oscillator?

What was the initial speed v_i?

## Homework Equations

Hooke's Law
Force = k*change in distance

Frequency - (1/2*pi)*sqrt(k/mass)

Total mechanical energy = potential energy + kinetic energy

Potential energy = 1/2*k*Amplitude^2

Kinetic energy = 1/2 * mass*v_max^2

## The Attempt at a Solution

F=k*change in x
20 = k*0.2
k = 100

Frequency= (1/2pi) * sqrt(k/m)
Frequency=(1/2pi) * sqrt (100/.5)
Frequency=2.251 Hz

For some reason the answer is 1.0 Hz but I can't figure out what I did wrong. Once I figure this one out I can move onto the next two.

Last edited:
I am confused! Why did you calculate k while it is given in the picture?

How is K given in the picture? Am I missing something? Which is totally possible. Is the 20 N/m the spring constant?

You can figure it out by determining its dimension :)

Yeah you were right. The spring constant was in fact labeled in the picture xD. I feel rather stupid now, especially since that was the only thing wrong :P. Oh well. Lesson learned - look at ALL the information. Haha. Thanks for the help!

Okay so I figured out the first part, and the second part (1.936) but now I'm stuck on the third part - finding the initial speed. I know that I should use v(t)=-vmax*sin(2*pi*frequency*t) but we don't know t. And a t of zero gives me an answer of zero...

you have 2 eq.:

x = A * cos(wt + phi)
v = vm * sin(wt + phi)

let t = 0 :)

## What is oscillation frequency?

Oscillation frequency refers to the number of complete cycles or vibrations per unit of time for a system that undergoes harmonic motion. It is typically measured in Hertz (Hz) and is inversely proportional to the period of the motion.

## How is oscillation frequency related to total mechanical energy?

The oscillation frequency is directly related to the total mechanical energy of a system. As the frequency increases, the total mechanical energy also increases. This is because the higher the frequency, the faster the system is oscillating and therefore, the more energy it possesses.

## What is total mechanical energy?

Total mechanical energy is the sum of an object's kinetic energy and potential energy in a given system. In the context of oscillation, it refers to the energy of the system as it oscillates back and forth between its kinetic and potential forms.

## How does initial speed affect oscillation frequency?

The initial speed of an object affects the oscillation frequency by determining the amplitude of the oscillations. Higher initial speeds result in larger amplitudes and therefore, a higher oscillation frequency. This is because a higher initial speed gives the object more kinetic energy, causing it to travel further from its equilibrium position before turning around.

## What is the relationship between initial speed and total mechanical energy?

The initial speed of an object is directly related to its total mechanical energy. A higher initial speed results in a higher total mechanical energy, as the object has more kinetic energy to contribute to the system's energy. Conversely, a lower initial speed results in a lower total mechanical energy.

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