Physics
posted by Zoe
A particle executes simple harmonic motion with an amplitude of 9.00 cm. At what positions does its speed equal two thirds of its maximum speed?
I got:
v2 +ω^2x^2 =ω^2A^2
vmax =ω A and v = ωA/2?

drwls
Since it executes SHM, the sum of potential energy and kinetic energy is a constant, with PE proportional to x^2 and KE proportional to V^2. This means
(x/A)^2 + (V/Vmax)^2 = 1
where A is the amplitude and x is the distance from the mean position.
When V/Vmax = 2/3,
(x/A)^2 = 1  4/9 = 5/9
x/A = (sqrt5)/3 = (+or) 0.7454
Respond to this Question
Similar Questions

Physics
A particle executes simple harmonic motion with an amplitude of 9.00 cm. At what positions does its speed equal two thirds of its maximum speed? 
Calculus
If the equation of motion of a particle is given by s = A cos(ωt + δ), the particle is said to undergo simple harmonic motion. (a) Find the velocity of the particle at time t. s'(t) =  A ω sin(ωt + δ) I figured … 
Cal
If the equation of motion of a particle is given by s = A cos(ωt + δ), the particle is said to undergo simple harmonic motion. s'(t) = Aω sin(ωt + δ) When is the velocity 0? 
Physics
A massspring system has b/m = ω0/2, where b is the damping constant and ω0 the natural frequency. How does its amplitude A when driven at a frequency 12% above ω0 compare with its amplitude at resonance Ares at ω0? 
physics
A horizontal spring mass system is set up to keep time so that it goes from one side to the other in 6 seconds. The mass used in this system is 0.69 kg. The distance from one side to the other is 2.4 m. What spring constant should … 
Physics
A circuit contains a selfinductance L in series with a capacitor C and a resistor R. This circuit is driven by an alternating voltage V=V0sin(ωt). We have L=0.015 H, R= 80 Ω, C= 5e06 F, and V0=40 volts. (a) What is the … 
Physics
Consider the following RLC series circuit. with V=5 Volts, R=15 Ohms, C=0.004 Farad, L=0.045 Henry. Define the frequencies ω± as the frequencies such that the absolute value of the current of the circuit I0(ω) equals 1/2*I0max. … 
Physics Help
A bungee jumper undergoes simple harmonic motion with amplitude 3.5 m and frequency 0.135 Hz. Assume the bungee jumper follows the simple harmonic motion equation x=Acos(wt). A. Determine the bungee jumper's velocity at 0.25 s B. Determine … 
physics
An 0.90 kg object is attached to one end of a spring, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the drawing. With the aid of these data, determine the following … 
Physics
The steadystate amplitude of a weakly damped forced oscillator is given by 2 2 2 2 2 2/1 0 0 [( ) 4 ] ( ) ω −ω + ω ω = b f a Depict it as a function of frequency and obtain expression for resonance frequency. …