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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 vibrationa) 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)

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

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.**