Physics
posted by Joe .
A mass is oscillating with amplitude A at the end of a spring.
How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?

x=A•sinωt
v =dx/dt = A•ω•cosωt
PE = KE
kx^2/2 = mv^2/2
k = m•ω^2
m•ω^2• (A•sinωt)^2/2 = m•( A•ω•cosωt)^2/2
(sinωt)^2 = (cosωt)^2
(tan ωt)^2 = 1
ωt = π/4
x=A•sinωt = A•sin(π/4) =0.707•A
Respond to this Question
Similar Questions

Physics Problem
A 3.00kg mass is fastened to a light spring that passes over a pulley. They pulley is frictionless, and its inertia may be neglected. The mass is released from rest when the spring is unstretched. If the mass drops 10.0cm before stopping, … 
Physics
I need help with part b, c, and d please! A 45 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to: y(t) = 1.4 * sin( 4 * t ) where y is measured in meters and t in seconds.  … 
Physics
I need help with b... I found that k=.750880 for part a but I can't figure out what y would be to get potential energy. A 52 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to: y(t) … 
physics
Which of the following statements is true about a mass, which is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface? 
physics
Suppose that a 200g mass (0.20kg) is oscillating at the end of a spring upon a horizontal surface that is essentially frictionfree. The spring can be both stretched and compressed and have a spring constant of 240N/m. It was originally … 
Physics
A thrillseeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched … 
physics
A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals a half the kinetic energy? 
Physics
In a horizontal springmass configuration, the position of the 0.52 kg mass is described by [x = (1.09 m) sin(2.70t)] a) What is in meters the amplitude of these oscillations? 
Physics
A tension spring opposes being stretched, but offers no resistance to being compressed (think of a slinky!). A tension spring, with an equilibrium length of 1.25 m, is suspended by one end from a ceiling at a height of 2.5 m above … 
Physics
A 0.50kg mass is placed on the end of a vertical spring that has a spring constant of 75 N/m and eased down into its equilibrium position. (a) Determine the change in spring (elastic) potential energy of the system. PEs=1/2kx^2=1/2(75)(0.5)^2=9.375 …