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.

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.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

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 spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.6 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.) x(t) =
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.
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