Oscillations help in physics please... best answers will be awarded?
The velocity of a simple harmonic oscillator is given by
v = -8.45sin(26.6t)
a) What is its angular frequency?
b) What is the amplitude of the motion in meters to two decimal places?
c) To the nearest hundredth of a meter where is the mass at the time t=27.84 seconds?
d) If the mass is 0.16 kg, what is the spring s potential energy to the nearest tenth of a joule
e) What is its kinetic energy to the nearest tenth of a joule?
- NCSLv 74 years agoFavorite Answer
Needing to assume some units, I'll assume m/s for velocity.
a) the coefficient of t in the trig argument -- here 26.6 rad/s
b) Because velocity is a sin function, displacement was a cos function.
x = Acos(26.6t) and
v = dx/dt = (-A * 26.6rad/s)sin(26.6t)
Therefore -A * 26.6rad/s = -8.45 m/s
A = 0.32 m
c) x = 0.32m*cos(26.6*27.84) → make sure you're in radians mode
x = 0.20 m
d) k = ω²m = (26.6rad/s)² * 0.16kg = 113.21 kg/s²
Presuming we're interested in the point where x = 144.62 m, then
SPE = ½ * 113.21kg/s² * (0.20m)² = 2.4 J
e) v = -8.45m/s*sin(26.6*27.84) = 6.47 m/s
KE = ½ * 0.16kg * (6.47m/s)² = 3.4 J
Bonus: so the total energy is 5.7 J.
Max KE = ½mVmax² = ½ * 0.16kg * (8.45m/s)² = 5.7 J √√√
Max SPE = ½kA² = ½ * 113.21kg/s² * (0.32m)² = 5.7 J √√√
Hope this helps!