A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = r/12, n/8, 1/6, x/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(7/12) = 0.666 X ft x(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x(x/4) = 0.663 X ft x(9x/32) = 0.662 X ft (b) What is the velocity of the mass whent = 37/16 s? 16 3 ft/s In which direction is the mass heading at this instant? upward o downward (c) At what times does the mass pass through the equilibrium position? + 16 X , n = 0, 1, 2, ...

A pulley-and-cable assembly supports a block W and it requires a force at P for equilibrium. Since block W has a mass of 30kg (g=9.806), calculate the force of the spring CD and the magnitude of force P.

A 5.75-kg mass stretches a vertical spring 0.5 m. If the spring is stretched an additional 1 m and released, how long does it take to reach the (new) equilibrium position again? (How do I find the amount of time?)

It compresses the spring 5.3 cm before coming to a stop.

A mass weighting 32 lbs stretches a spring 8 inches. The mass is in a medium that exerts a viscous resistance of 38 lbs when the mass has a velocity of 4 ft/sec. Suppose the object is displaced an additional 6 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) =

A mass weighting 16 lbs stretches a spring 6 inches. The mass is in a medium that exerts a viscous resistance of 1 lbs when the mass has a velocity of 2 ft/sec. Suppose the object is displaced an additional 3 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) =

A  3kg weight is attached to a spring with constant k= 48 kg /m and subjected to an external force F(t) = 42 cos(3t). The weight begins at rest in its equilibrium position. Find its displacement for t>0 , with y(t) measured positive upwards.

If the mass is 48kg and the spring constant is 12n/m,what is the period of oscillation?

A simple pendulum oscillates with a frequency of 6.1 Hz.  How long (in centimeters) is the pendulum?

A mass m = 1.9 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.05 Hz. Part (a)  Write an equation for the spring constant k.   Part (b)  Calculate the spring constant k, in Newtons per meter.  Part (c)  Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement.  Part (d)  Calculate the total mechanical energy E, in joules.