What is the velocity of an oscillator at a specific position?

In summary, when a simple harmonic oscillator with a spring constant of 7.8 N/m, an amplitude of 12 cm, and a maximum speed of 4.3 m/s is at x = 5.4 cm, its speed is -0.003764 m/s. This was found by using the equations for maximum kinetic energy, kinetic energy, acceleration, and velocity in that order. However, the resulting answer was incorrect.
  • #1
Capncanada
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Homework Statement



A simple harmonic oscillator has spring constant k = 7.8 N/m, amplitude A = 12 cm, and maximum speed 4.3 m/s.
What's the oscillator's speed when it's at x = 5.4 cm?


Homework Equations



KE_max=1/2*k*A^2
KE=1/2mv^2
ma=-kx
v=k/ma

The Attempt at a Solution



I used each equation in order to find the K_max, the mass of the oscilator, the acceleration, and then the velocity in that order, but the answer I got was wrong.
 
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  • #2
K_max=1/2(7.8N/m)(0.12m)^2= 0.00588Jm=KE_max/1/2v^2= 0.00588J/1/2(4.3m/s)^2= 0.000368kga=-kx/m=-7.8N/m(0.054m)/0.000368kg=-2080m/s^2v=k/ma=7.8N/m/(-2080m/s^2)= -0.003764m/s
 

1. What is an oscillator?

An oscillator is a physical system that exhibits periodic motion. This means that it repeats the same motion over and over again at regular intervals.

2. How is velocity of an oscillator defined?

The velocity of an oscillator is defined as the rate of change of its displacement with respect to time. It is a measure of how fast the oscillator is moving at any given moment.

3. What factors affect the velocity of an oscillator?

The velocity of an oscillator is affected by its amplitude (maximum displacement), frequency (rate of oscillation), and damping (resistance to motion). These factors determine the speed and smoothness of the oscillator's motion.

4. What is the relationship between velocity and displacement of an oscillator?

The velocity and displacement of an oscillator are directly related. As the displacement of an oscillator increases, its velocity also increases. Similarly, as the displacement decreases, the velocity decreases. This relationship can be described by the oscillator's amplitude and frequency.

5. How can the velocity of an oscillator be measured?

The velocity of an oscillator can be measured using tools such as a stopwatch and a ruler or a motion sensor. By measuring the displacement of the oscillator at different time intervals, the average velocity can be calculated. Additionally, the velocity can also be determined from the oscillator's equation of motion.

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