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 x= .4 meter, and force by the spring, F= -16 nt. (Note that as the free end moves in +x direction the spring's force toward -x direction becomes more negative.) PART a. Make a graph of F(x) from x=0 to x= .8 m. From your graph of F vs x, find the slope of the line. This slope is defined as the 'force constant', k, a property of the spring. PART b. With the force c... click for more

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 x= .4 meter, and force by the spring, F= -16 nt. (Note that as the free end moves in +x direction the spring's force toward -x direction becomes more negative.) PART a. Make a graph of F(x) from x=0 to x= .8 m. From your graph of F vs x, find the slope of the line. This slope is defined as the 'force constant', k, a property of the spring. PART b. With the force ... click for more

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 the above function represents position x, its derivative would be the rate of change of position, namely the velocity. Take the derivative to write v(t). PART c. Similarly, the derivative of v(t) is the acceleration, a(t). Take the derivative to express a(t). PART d. Note that in a(t), the right side of x(t) can replace all parameters past w^2. Use this to eliminate... click for more

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 showing parameters. PART a. Apply the second law, 'net force = ma' to the moving mass at position x. Expressing the acceleration a as the second derivative of x, write an equation (1) in terms of only parameters k, M, and x. (HINT: This equation is a second order differential equation. One solution for it is of the form (2) x= A cos (omega t) in which constants A, a... click for more

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 terms of given parameters, write (1) x(t), (2) v(t) and (3) a(t). PART b. Given values are: M= 4.32 kg, m= 1.44 kg, S= 2.4 m/sec, k= 64 nt/m. Calculate the following for the moving combined mass: initial velocity vo, angular frequency (omega); Period T; amplitude xm; position x at t= .6 sec; velocity v at t= 1.5 sec.