Simple Harmonic Motion (SHM) question check

saraht4bysion

1. Homework Statement
A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s.
calculate;
(I) the spring stiffness, k. (force per unit extension)
(II) the maximum velocity of the sphere as it oscillates.
(III) the maximum acceleration of the sphere as it oscillates.

2. Homework Equations
ω=2*∏/T

3. The Attempt at a Solution
my workings;
(I) W=2*∏/T
=2*∏/1.67

w^2=m/k
3.76^2=0.20/k
k=0.20/3.76^2
= 0.20/14.14
k=1.41*10^-2 Nm-1

(II) Vmax= +- W √A^2 - x^2
but x=0 so
Vmax= +- WA
= +- 3.79 * 0.030
Vmax= +- 1.13*10^-1 ms-1

(III) amax= +- W^2 * x
but x=A so
amax= +- W^2 * A
= +- 3.76^2 8 0.030
amax= +- 4.24*10^-1 ms-2

could you please check my answers for me, because, i don't know why, i just feel like I've gone wrong somewhere.
thanks sarah x
1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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Simon Bridge

Homework Helper
Welcome to PF;

(I) Reasoning looks OK.
How did you calculate T=1.67(s?)
In 12 seconds you get 20 cycles - how much time for one cycle?

Usually better to combine equations before putting the numbers in - to avoid rounding errors.

(II) and (III) OK reasoning ... you should keep the direction (+/-) since they ask for "velocity" rather than speed.

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