8. A force of 2 N stretches a spring by 10 cm. A mass of 0.2 kg is attached to the spring, and then the system is submerged in a medium that provides a damping force equal to four times the instantaneous velocity. Find the equation of motion, if at time t = 0, the mass is released from rest at a point located 5 cm above the equilibrium position. Will the mass pass through the equilibrium position? (Use g = 9.8 m/s²) Sol.

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.

A spider can tell when its web has captured, say, a fly because the fly's thrashing causes the web threads to oscillate. A spider can even determine the size of the fly by the frequency of the oscillations. Assume that a fly oscillates on the capture thread on which it is caught like a block on a spring. What is the ratio of oscillation frequency for a fly with mass m to a fly with mass 2.5m?

Please help find T1.

A mass suspended from a spring is raised a distance of 5 cm above its resting position. The mass is released at time t=0 and allowed to oscillate. After one third of a ​second, it is observed that the mass returns to its highest position, which was 4.5 cm above its resting position. What is the rate of change of the position of the mass at t = 2.1 seconds? Round your answer to three decimal places.

Vector u = <-7,3,-5> and vector v = <-1,1,0>. Find the cross product of 9(u X v)

A 3 kg block attached to a spring with a spring constant of 9 N/m oscillates horizontally on a frictionless table. Its velocity is 7 m/s when x0 = 0.39 m. What is the block's maximum acceleration (in m/s^2)?

Answer..

A mass of 6.33 kg is placed on a vertical spring.  What is the spring constant, in N/m, of a mass-spring system with a period of 0.6 s?

A 210 g air-track glider is attached to a spring. The glider is pushed in 8.8 cm against the spring, then released. A student with a stopwatch finds that 12 oscillations take 11.5 s. What is the spring constant? Express your answer in newtons per meter. k= VE ΑΣΦ ? N/m