- #1
rikiki
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Homework Statement
A mass of 0.3kg is suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released, for resulting vibration, calculate:
a) the frequency of vibration
b) the maximum velocity of the mass during the vibration
c) the maximum acceleration of the mass during the vibration
Homework Equations
Angular frequency= √((Spring constant)/mass)
Frequency= (Angular frequency)/(2 × π)
Velocity: v(t) = -ωA sin(ωt + φ)
Acceleration: a(t) = -ω 2 A cos(ωt + φ)
Displacement = amplitude x sin(angular frequency x time)
T=1/f
The Attempt at a Solution
a) Angular frequency= √((Spring constant)/mass)
ω_n= √(k/m)
ω_n= √(200/0.3)
ω_(n )=25.8199
Frequency= (Angular frequency)/(2 × π)
F= ω_n/2π
F= 25.8199/2π
F=4.11Hz
b) Velocity= -angular frequency ×amplitude ×sin〖(angular frequency ×time + phase constant〗
v(t)= -ωA sin(ωt+φ)
angular frequency=25.8199
amplitude=0.01m
phase constant= ?
time = 0.243
My physics is pretty poor I'm afraid, and i'd be grateful for any help possible. I've become stuck trying to calculate the phase constant. I've read that through using x = A*sin(ωt + φ), and setting t to 0, I can calculate what the phase constant should be. I seem to keep getting 0 as my result here however.Any help on how the phase constant should be calculated would be grately appreciated. Thanks.