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## 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.

## Homework Equations

ω=2*∏/T

## The Attempt at a Solution

my workings;

(I) W=2*∏/T

=2*∏/1.67

W= 3.76rads-1

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