Question

Notify Me Bookmark

A mass of 8 kg is attached to the end of a spring with a natural length 0.6 m. A force of 128 N is required to maintain the spring stretched to the length of 1 m in the positive x direction beyond the equilibrium point at x = 0. It is stretched to a length of 1 m and then released with initial velocity 0 . Find the position x(t) of the mass at any time t. x(t) =

A mass of 8 kg is attached to the end of a spring with a natural length 0.6 m. A force of 128 N is required to maintain the spring stretched to the length of 1 m in the positive x direction beyond the equilibrium point at x = 0. It is stretched to a length of 1 m and then released with initial velocity 0 . Find the position x(t) of the mass at any time t. x(t) =

Image text
A mass of 8 k g is attached to the end of a spring with a natural length 0.6 m . A force of 128 N is required to maintain the spring stretched to the length of 1 m in the positive x direction beyond the equilibrium point at x = 0 . It is stretched to a length of 1 m and then released with initial velocity 0 . Find the position x ( t ) of the mass at any time t .
x ( t ) =
◻

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

A mass of 0.5 kg is attached to the end of a spring. To stretch the spring 2 m in the positive x direction beyond its equilibrium position, a force of 144 N must be applied. The mass is then pulled x(0) = 0.8 m from equilibrium position and set in motion with an initial velocity of −12 m/s. Find the position x(t) of the mass at any time t. x(t) =
Solution
0 0

A spring (which behaves linearly both in tension and compression) when tested vertically in isolation, as shown in Figure 1, is found to stretch by x0 cm when it supports a mass of m1 kg. Figure 1 The spring extends by x0 cm when supporting an m1 kg mass The spring, along with a damper, is then attached horizontally to a trolley of mass 1360 kg, which is constrained to move only in the x-direction (see Figure 2). The spring is stretched some distance from its equilibrium position before being released. (a) (b) Figure 2 (a) A frictionless trolley is attached by a spring, with spring constant k and a damper with a damping coefficient χ. The trolley is shown in its natural rest position with its left-hand face at x = 0. (b) Free body diagram for the trolley shortly after being pulled to the right then released, with the spring under tension so, at this instant, its velocity is in the negative x-direction. (For clarity the damping force and normal reaction forces have been shown as acting at the point of their arrows - the spring force and weight are shown as acting at the tail of their arrows.)
Solution
0 0

A block, whose mass is 0.620 kg, is attached to a spring with a force constant of 128 N/m. The block rests upon a frictionless, horizontal surface (shown in the figure below). The block is pulled to the right a distance A = 0.120 m from its equilibrium position (the vertical dashed line) and held motionless. The block is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the block? N (b) At that very instant, what is the magnitude of the block's acceleration (in m/s2 )? m/s2 (c) In what direction does the acceleration vector point at the instant of release? Away from the equilibrium position (i. e. , to the right in the figure). The direction is not defined (i.e., the acceleration is zero). Toward the equilibrium position (i.e., to the left in the figure). You cannot tell without more information.
Solution
0 0