Graph a given record of force vs end location, for a certain spring, find its force constant. Develop F(x) and PE(x).

On a frictionless table, one end of a spring is fixed. A cord attached to the free end pulls it along a meter scale beginning from 0. A record is made of the position of the free end, x, and the resisting force, F, exerted by the spring on the cord. SEE ATTACHMENT #1 for the parameters and a record of F vs x, showing position ...continues

Graph a given record of force vs end location, for a certain spring, find its force constant. Develop F(x) and PE(x).

On a frictionless table, one end of a spring is fixed. A cord attached to the free end pulls it along a meter scale beginning from 0. A record is made of the position of the free end, x, and the resisting force, F, exerted by the spring on the cord. SEE ATTACHMENT #1 for the parameters and a record of F vs x, showing position ...continues

Simple Harmonic Motion defined by a reference circle from which come five SHM equations.

Point P is moving in a circle at constant speed. On a diameter on the x axis, point Q moves in such a way that the x coordinates of both P and Q remain the same. SEE ATTACHMENT #1 for a diagram and explanation of parameters. PART a. First with parameters then with numbers, express x as a function of time. PART b. Since th ...continues

General equations of SHM of a mass attached to a spring on a horizontal frictionless table.

On a frictionless table, mass M is attached to the free end of a spring whose force constant is k. The free end is located at the origin of an x axis. The other end of the spring is fixed. Now the mass is moved toward +x to position the free end at xm, and at that point is released from rest. SEE ATTACHMENT #1 for a diagram sho ...continues

Moving mass m collides with stationary mass M attached to a spring on a frictionless table. Write SHM equations.

On a horizontal, frictionless table, a mass M is attached to the free end of a spring with the other end fixed. Another mass, m, moving at velocity S, collides and sticks to mass M and at that point, SHM begins. The spring's force constant is k. SEE ATTACHMENT #1 for a diagram of parameters and a reference circle. PART a. In t ...continues

Compare a simple pendulum's period on the earth to its period on a moon to find the moon's gravity acceleration.

A simple pendulum, length L, completes 12 oscillations in 30 seconds here on the earth where g= 9.8 nt/kg. The same length pendulum on a certain moon of Jupiter, completes 18 oscillations in 54 seconds. a.) Find the acceleration of gravity, g1, on that moon. b.) Find the weight on the surface of that moon, of a person w ...continues

An irregular flywheel is suspended on a pivot and oscillates with SHM from which we must find its moment of inertia.

A flywheel is symmetrical but irregular. SEE ATTACHMENT #1 for a diagram showing parameters. Its mass is 25 kg. When supported from a knife edge pivot, .36 m from the c. m. at its center, it oscillates as a physical pendulum completing 100 complete oscillations in 180 seconds. Find Io, its moment of inertia about the c.m. axis ...continues

Given an equation of x(t) for a certain point moving with SHM, get v(t) and a(t), then calculate intercepts on the curves provided in ATTACHMENTS.

The position x of a certain SHM is expressed by: x = (.25 m) cos (8 t). PART a. Take derivatives to write v(t) and a(t). PART b. ATTACHMENT #1 shows general sine or cosine curves with the time axis shown. The location of the vertical axis, not shown, depends on the equation for t=0. For each equation, make a vertical axis ...continues

For a given equation x(t) of SHM with initial phase non-zero, obtain v(t) and a(t) then make graphs of all three functions. Must show intercepts.

The position x of a certain SHM is expressed by: x = (.36 m) cos (6 t + .628). PART a. Take derivatives to write v(t) and a(t). PART b. ATTACHMENT #1 shows general sine or cosine curves with anly a time axis. The location of the vertical axis, not shown, depends on the equation. For your x(t) and v(t) and a(t), locate the ve ...continues

Calculating the moment of inertia of an irregular object by the axis translation theorem.

An irregular piece of sheet metal mounted on a pivot at a distance of .62 m from the cm. About this pivot point, it oscillates with SHM with a period measured at 2.25 seconds. PART a. Find the moment of inertia about the pivot axis. PART b. Find the moment of inertia about the cm axis.