A mass m is on an inclined plane at angle theta, as shown above. Attached to the

Question

A mass m is on an inclined plane at angle theta, as shown above. Attached to the mass is a spring of spring constant k that is fixed at the top of the incline. There is gravity in the problem.

A.) Assuming a coefficent of friction mu, find the Equation of Motion for the system using cartesian coordinates in fram A.

B.) Solve the Equation of Motion assuming no friction with initial conditions x(0) = x_0 (x subscript 0) and xdot(0) = xdot_0 (xdot subscript 0)

A mass m is on an inclined plane at angle theta, as shown above. Attached to the mass is a spring of spring constant k that is fixed at the top of the incline. There is gravity in the problem. Assuming a coefficent of friction mu, find the Equation of Motion for the system using cartesian coordinates in fram A. Solve the Equation of Motion assuming no friction with initial conditions x(0) = x_0 (x subscript 0) and xdot(0) = xdot_0 (xdot subscript 0)

Explanation / Answer

normal reaction acting on block, N = [m*g*cos(theta)] (a2) friction force, f = mu*N = [mu* m*g*cos(theta)] (-a1) force exerted by spring on block, Fs = [k*x] (-a1) where, x = elongation in spring force by gravity, Fg = [m*g*sin(theta)] (a1) a). for equilibrium of block along the incline; Fg = Fs + f => mg*sin(theta) = k*x + mu*mg*cos(theta) => x = mg*[sin(theta) - mu*cos(theta)]/k b). when f = 0 x = mg*sin(theta)/k

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