Question

Notify Me Bookmark

A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is x(t) = 10 sin⁡(t), where t is in seconds and x is in centimeters. (a) Find the velocity and acceleration at time t. (b) Find the position, velocity, and acceleration of the mass at time t = π/3. In what direction is the mass moving at that time?

A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is x(t) = 10 sin⁡(t), where t is in seconds and x is in centimeters. (a) Find the velocity and acceleration at time t. (b) Find the position, velocity, and acceleration of the mass at time t = π/3. In what direction is the mass moving at that time?

Image text
A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is x ( t ) = 10 sin ⁡ ( t ) , where t is in seconds and x is in centimeters. (i) (a) Find the velocity and acceleration at time t . (b) Find the position, velocity, and acceleration of the mass at time t = π / 3 . In what direction is the mass moving at that time?

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 on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is x(t) = 4 sin⁡(t), where t is measured in seconds and x in centimeters. (a) Find the velocity and acceleration at time t. v(t) = a(t) = (b) Find the position, velocity, and acceleration of the mass at time t = 2π/3. x(2π 3) = v(2π 3) = a(2π 3) = In what direction is the mass moving at that time? Since v(2π 3) 0, the mass is moving to the
Solution
0 0

An object oscillates with simple harmonic motion along with x axis. Its displacement from the origin varies with time according to the equation x = (4.00 m)cos⁡(πt + π/4) Where t is in seconds and the angles in the parentheses are in radians. (a) Determine the amplitude, frequency and period of the motion. (b) Calculate the velocity and acceleration of the object at time t. (c) Using the results in part(b), determine the position, velocity and acceleration of the object at t = 1.0 s (d) Determine the maximum speed and acceleration of the object.
Solution
0 0

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x′(t) is its velocity, and x′′(t) is its acceleration. A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = 2cos⁡(t). At the time t = 0, its position is x = 7. (a) Find the velocity and position functions for the particle. v(t) = f(t) = (b) Find the values of t for which the particle is at rest. (Use k as an arbitrary non-negative integer. ) t =
Solution
2 0