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saraht4bysion
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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