HELP! Oscillation Problem Solution

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In summary, the conversation is about finding the maximum acceleration, maximum speed, and position of an object at these maxima using the equation of motion y(t)=2.0cos(0.5t+pi/4)meter. The conversation also discusses finding the speed of the object when it is +1.2m from its equilibrium position and calculating the kinetic, potential, and total energies at that point. The main point of confusion is what is meant by "maximum" and how to find the mass for the energy equations.
  • #1
Kudo Shinichi
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HELP!A problem on oscillation

Homework Statement
the equation of motion of an object is y(t)=2.0cos(0.5t+pi/4)meter
a) Find its maximum acceleration and maximum speed, and its position at the time of these maxima.
b) what is the speed of the object when it is +1.2m from its equilibrium position?
c) what are the kinetic potntial and total energies at that point?


The attempt at a solution
a) for this part I don't reall understand what does the question mean by the maximum, is it when cos equals to 1?
b) derive 2.0cos(0.5t+pi/4), which equals to -2sin(0.5t+pi/4)*0.5=-1sin(0.5t+pi/4)
then plug the 1.2 into the unknown variable, which equals to -sin(0.5*1.2+pi/4)=-0.98 I don't really think it is the correct solution for this part
c) I have to find out the correct v from part B and plug into both kinetic and potential energy equation, but I have one more problem here, which is how do i get mass for this question?
P((1/2mv^2)i) + K(1/2mv^2)i) = P((1/2mv^2)f) + K(1/2mv^2)f)

Thank you for helping me.
 
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  • #2


You're given the equation for motion.

velocity is the first derivative.

acceleration is the second derivative.

At what value of t then do each of these functions reach their max?
 
  • #3


LowlyPion said:
You're given the equation for motion.

velocity is the first derivative.

acceleration is the second derivative.

At what value of t then do each of these functions reach their max?

Sorry, but i still don't quite understand what does max mean, does it mean that when cos or sin equals to 1?
 
  • #4


Kudo Shinichi said:
Sorry, but i still don't quite understand what does max mean, does it mean that when cos or sin equals to 1?

I'd say so.
 

FAQ: HELP! Oscillation Problem Solution

1. What is oscillation?

Oscillation is a repetitive back-and-forth motion or movement around a central point or equilibrium position. It can be seen in various natural phenomena, such as the swinging of a pendulum or the vibration of a guitar string.

2. What causes oscillation?

Oscillation is caused by a restoring force that acts to bring a system back to its equilibrium position when it is displaced. This force could be gravity, tension, or elasticity, depending on the specific system.

3. How is oscillation measured?

Oscillation can be measured using various methods, depending on the type of oscillation. For example, the amplitude (maximum displacement from equilibrium) and period (time for one complete oscillation) can be measured for a pendulum, while the frequency (number of oscillations per second) can be measured for a vibrating string.

4. What factors can affect oscillation?

The factors that can affect oscillation include the mass of the system, the strength of the restoring force, and any external forces acting on the system. Changes in these factors can alter the amplitude, frequency, and period of oscillation.

5. How is oscillation used in science and technology?

Oscillation has many practical applications in science and technology. It is used in clocks, watches, and other timekeeping devices. It is also used in engineering to design structures that can withstand vibrations, such as bridges and buildings. In physics, oscillation is studied to understand the behavior of waves and energy transfer.

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