A 3 kilogram weight stretches a spring by 8 cm. The mass-spring system is immersed in a damping fluid which exerts a force of 0.5 N when the mass is traveling 0.25 m/sec. Write a differential equation for u(t), the displacement of the mass at time t. (use g = 9.8 m/sec ^2 .)

A force of 6 N will hold a spring stretched at 3 m. Suppose a 6 kg mass is attached to the spring, it is stretched to 3 m, and released with an initial velocity of 0 m/s. Assume there is no dampening. Find an equation involving y (position) and v (velocity, which is the derivative of position) that governs the motion of the mass.

A mass of 1.79 kg is placed on a vertical spring.  What is the spring constant, in N/m, of a mass-spring system with a period of 0.7 s?

H In a damped oscillator, let m = 250 g, k=85 N/m, and b=0.070 kg/s. In how many periods of oscillation the mechanical energy of the oscillator drop to one-half of its initial value?

A 1.3 kg block is attached to a spring with spring constant 13 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 39 cm/s. Part A: What is the amplitude of the subsequent oscillations? Part B: What is the block's speed at the point where x=0.40 A?

In a spring-mass experiment, a hanging spring is stretched by 5 cm when a mass of 156 g object is attached to it. When the mass is put to oscillate, the sensor measured a maximum speed of 3.84 m/s. Take g = 9.8 m/s². b) What is the spring constant value? At what position(s) will the object have a speed 1/2 that of the maximum speed? Take y = 0 at the equilibrium and upward is a positive direction. At t = 0, the object is moving at 1/2V max away from the equilibrium with the spring compressed. Using y (t) = A cos(wt + 0), write a complete expression with numerical values and units to describe the motion of the object.

Your grandfather clock's pendulum has a length of 0.9930 m. a. If the clock runs slow and loses 23 s per day, how should you adjust the length of the pendulum? Note: due to the precise nature of this problem you must treat the constant g as unknown (that is, do not assume it is equal to exactly 9.80 m/s2). Express your answer to two significant figures and include the appropriate units. Enter positive value in case of increasing length of the pendulum and negative value in case of decreasing length of the pendulum.

A 0.282 kg mass is attached to a spring with a spring constant 197 N/m so that the mass is allowed to move on a horizontal frictionless surface. The mass is released from rest when the spring is compressed 0.145 m. Find the maximum force on the mass. Answer in units of N.

8. A weight of 0.5kg stretches a spring by 0.49m. The spring-mass system is submerged in delicious melted butter with a damping coefficient of y=4. The spring is then lowered by an additional 1.0m and released with velocity 0. There is no external force. Find the function which gives the location of the weight at time t. Note: I have designed this to work out nicely. If it's not working out nicely then you probably got some butter in your calculations.

A mass weighting 24 lbs stretches a spring 4 inches. The mass is in a medium that exerts a damping force of 57 lbs when the mass has a speed of 6 ft/sec. Suppose the object is displaced an additional 8 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) = Use the convention: If the displacement is upward then u <0