# Solve questions on oscillations and kinetic energy

• SWoo
In summary, the conversation discusses three different scenarios involving springs and oscillations. In the first scenario, a spring of constant k is attached to a block of mass M and a block of mass m collides in-elastically with M, causing it to compress the spring. In the second scenario, a sphere attached to a spring is moved by a small amount and goes into oscillation, and in the third scenario, a bar suspended by a spring is also in oscillation. The conversation provides equations and hints for solving the questions related to these scenarios.
SWoo
Thread moved from the technical forums, so no HH Template is shown.
A spring of spring constant k sits on a frictionless horizontal table, one end of the spring is attached to a wall the other end to a block of mass M= 2kg, also resting on the frictionless table. Another block of mass m=450g moving at a speed of 7m/s collides in-elastically with the block of mass M, as a result of the collision M moves in such a direction so as to compress the spring, which takes 0.4 seconds to reach maximum compression.

for a. what happens before removing M is that it oscillates alone and has separated from m. which is why now, you can remove M.
a. You now remove M when the system is at the point where v=0, How much time does it take for the mass M to go from having one third of its maximum kinetic energy to having 1/5 of its maximum kinetic energy as it is moving away form equilibrium.

doubling the mass doubles the energy so using the equation 1/2(2m)(v)^2=mv^2, you know that the Ek is changed by a factor of 2. however, apparently this is wrong. any ideas on how to solve it? to help solve the question, here are some hints:https://gyazo.com/2d8e1281d78037d5c8e0427075a23f00

b. The sphere of mass M and radius R shown rolls without slipping on the ground. It is attached at the top to a spring of spring constant k. The other end of the spring is attached to a wall. The system is in equilibrium, then you move the sphere by a small amount and the system goes into oscillation, find the period for small oscillations in terms of the quantities given.

I used this equation to solve the second part, but again, not getting the right answer. w0 = square root of mgR/I. Hints: https://gyazo.com/5d49cbb19ab59b85ec336f2205af7e23

c. A bar of length L is suspended from its top edge where it is free to rotate about the pivot, its bottom is connected to a horizontal spring of spring constant k the other end of the spring is connected to wall. Find the period of small oscillations for this bar.

used the same equation as b. hints: https://gyazo.com/d3b5f13dfed5554a037d0767977b8389

Hi again and again,

We still want some effort from you: there's no point in robbing you of the exercise by doing it for you. And to help you work through we need to know what you can muster yourself so we can try to be effective in nudging you towards understanding.

Last edited:
SWoo said:
You now remove M
Do you mean remove m?
SWoo said:
what happens before removing M is that it oscillates alone and has separated from m. which is why now, you can remove M.
Assuming you mean remove m, it says to remove it when the velocity of the masses first reaches zero, not the second time it reaches zero.
SWoo said:
doubling the mass
I see no mention of doubling a mass.

First step is to figure out the velocity of the masses just after impact.

For b and c, please post a separate thread for each independent question. You should fill in the template, showing any relevant standard equations or principles, and, as BvU says, show some attempt.

## What are oscillations?

Oscillations are repetitive back and forth movements around an equilibrium point. They can occur in various systems, such as pendulums, springs, and sound waves.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object, and is represented by the equation KE = 1/2 mv^2.

## How are oscillations and kinetic energy related?

Oscillations involve the exchange of potential and kinetic energy. As an object moves back and forth, it alternates between having more potential energy (at the extremes of its motion) and more kinetic energy (at the equilibrium point). This relationship can be described by the law of conservation of energy.

## What factors affect the frequency of oscillations?

The frequency of oscillations is affected by the mass, stiffness, and length of the system. A heavier mass, stiffer material, and longer length will result in a lower frequency, while a lighter mass, more flexible material, and shorter length will result in a higher frequency.

## How is the period of oscillations calculated?

The period of oscillations is the time it takes for one complete cycle of motion. It can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant (or stiffness) of the system.

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