T, simple harmonic motion, gravity

In summary, there are two masses, M and -a, located at a distance of a from the origin on the y-axis. A third mass, m, is located at a distance of x from the origin and will oscillate back and forth due to gravity. To find the velocity of m when it reaches the origin, use the equation PE = GMm/(x^2 + a^2)^1/2 and equate it to KE at the origin. Solve for v to find the velocity at the origin.
  • #1
kjavia795
1
0
There are two masses both M +a and -a apart with respect to the origin on the y axis. A third mass, m, is x away from the origin. Due to gravity it will oscillate back and forth. What is T
Also, how can I use conservation of energy to find the velocity of the third mass m when it reaches the origin if it started at rest?

so far i got

g=2Gmx/(x^2+a^2)^(3/2)


and for the conservation of energy the PEi has to equal KEf
 
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  • #2
Hi kjavia, welcome to PF.
Potential energy at any point along the x-axis is given by
PE = GMm/(x^2 + a^2)^1/2.
Equate this to KE at the origin and find v.
 

Related to T, simple harmonic motion, gravity

1. What is "T" in simple harmonic motion?

"T" refers to the period of a simple harmonic motion, which is the time it takes for one complete cycle or oscillation of the motion. It is measured in seconds.

2. How is simple harmonic motion related to gravity?

Simple harmonic motion is a type of motion that occurs when a restoring force (such as gravity) acts on an object, causing it to oscillate back and forth around an equilibrium point. The motion is called "simple" because the restoring force is directly proportional to the displacement of the object from its equilibrium point.

3. How does the mass of an object affect its simple harmonic motion?

The mass of an object does not affect the period or frequency of its simple harmonic motion. However, it does affect the amplitude (maximum displacement) of the motion, as well as the amount of energy required to sustain the motion.

4. Can simple harmonic motion occur without gravity?

Yes, simple harmonic motion can occur without gravity if there is another restoring force acting on the object, such as a spring force. However, gravity is the most common and easily observable source of restoring force for simple harmonic motion.

5. What are some real-life examples of simple harmonic motion?

Some common examples of simple harmonic motion include a pendulum, a mass on a spring, a rocking chair, and a mass bouncing on a trampoline. Simple harmonic motion can also be observed in the motion of molecules in a solid or gas, as well as in sound waves.

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