A body weighing 25 lb is suspended from a spring of constant k = 160 lb /ft. At time t = 0 it has a downward velocity of 2 ft /sec as it passes through the position of static equilibrium. Determine (a) the system period and (b) the maximum acceleration attained by the mass.

A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft

When Crates A and B of mass ma = 31 kg and mB = 78 kg are released from rest, Crate A moves to the right on a rough surface (u = 0.4 ). The force P = 20 Newtons is always acting on Crate B. The linear spring has a stiffness of k = 490 N and is initially stretched 0.4 meters before the system is released from rest. Neglect the mass of the pulleys and cables and neglect friction in the pulley bearings. Determine the work done by the weight of Crate B (in Joules) when Crate A has moved a distance of 0.8 meters to the right. Consider g = 10 m. 82 B

Bar AB in the figure rotates counterclockwise with a constant angular velocity of 2.5 rad/s. If all of the bars have a unit mass of 2 kg/m, determine the total kinetic energy of the system in the position shown.

3: A 24 lb weight stretches a spring 6 feet. The weight hangs vertically from the spring and a damping force numerically equal to 2√√3 times the instantaneous velocity acts on the system. The weight is released from 3 feet above the equilibrium position with a downward velocity of 14 ft/s. (a) Determine the time (in seconds) at which the mass passes through the equilibrium position. (b) Find the time (in seconds) at which the mass attains its extreme displacement from the equilibrium position.

H4.

3. A block with a mass of 12 kilograms is attached to a horizontal spring with a spring constant of 100 newtons per meter. Initially the block is held at rest in place so that the spring is stretched 0.1 meters past its equilibrium point (we will use the stretched direction as the positive direction for the position). For the first 2 seconds, an external force of 4 newtons in the stretched direction is applied before the external force is shut off. (a) external force, find the value of the drag coefficient (you do not need to worry about units). Assuming that the oscillation would be in the critical damping case if there was no (Ъ) block in meters at time t seconds. DO NOT SOLVE THE INITIAL-VALUE PROBLEM! Give the initial-value problem modeling this scenario where r(t) is the position of the

. An object of mass 12 kg is suspended from a pulley which has a mass of 6 kg and a radius of rotation of 0.25 m. If at that time the pulley rotates with an angular velocity of 5 rad/s, we want to know that when the object moves down a distance of 2 m, then at what speed is the pulley rotating? If the friction force on the pulley bearing produces a moment of resistance of 2 N-m 12 kg 0.3 m

mechanical principles Explain the natural frequency of vibration in a mass-spring system.

A mass weighing 4 pounds is attached to a spring whose constant is 2 ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equlibrium position with a downward velacity of 12 t/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g -32 /s for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in t) of the mass at this instant? ft