Shm

a spiral spring of natural length 300mm is suspended vertically from a fixed point with its upper end fixed. a mass of 0.150kg is suspended at rest from the lower end of the spring to increase its length to 355mm, and released from rest so it oscillates about the equilibrium.

claculate:

a) Stiffness

b) Time period of oscillations

c) Max speed and KE of mass

i can do a and b but not c

what do i do?

Reply 1

Richie90

1

Daxx

a spiral spring of natural length 300mm is suspended vertically from a fixed point with its upper end fixed. a mass of 0.150kg is suspended at rest from the lower end of the spring to increase its length to 355mm, and released from rest so it oscillates about the equilibrium.

claculate:

a) Stiffness

b) Time period of oscillations

c) Max speed and KE of mass

i can do a and b but not c

what do i do?

Vmax occurs when there is no acceleration. If you've worked out the time period of oscillation then you should be able to use the formula:

Vmax = 2*pi*frequency*amplitude

Max KE is then calculated using the Vmax and the mass of the spring!

Hope that helps! :smile:

Reply 2

Operator

OP: Just to let you know where Richie90 got this formula (see below) from:

Richie90

Vmax = 2*pi*frequency*amplitude

You can either use the formula

v^2 = \omega^2(A^2 - x^2)

and say that

v = v_{\rm max}

when

x=0.

This gives

v_{\rm max} = A\omega,

with

\omega\equiv 2\pi f.

Alternatively, you can equate the maximum kinetic energy of the spring to the maximum potential energy of the spring, since energy is conserved during SHM. Doing this gives

\frac 1 2 mv_{\rm max}^2 = \frac 1 2 kA^2 \Rightarrow v_{\rm max} = A\omega,

where

\omega \equiv \sqrt{k/m} \equiv 2\pi f.

Reply 3

tylerplatt

9

Original post by Daxx

a spiral spring of natural length 300mm is suspended vertically from a fixed point with its upper end fixed. a mass of 0.150kg is suspended at rest from the lower end of the spring to increase its length to 355mm, and released from rest so it oscillates about the equilibrium.

claculate:

a) Stiffness

b) Time period of oscillations

c) Max speed and KE of mass

i can do a and b but not c

what do i do?

Can you tell me how do all of them

Reply 4

Joinedup

20

Original post by tylerplatt

Can you tell me how do all of them

This thread was started when Gordon Brown was still enjoying a honeymoon period as Prime Minister and everyone still thought investment banks were on the level.

You'll need to correctly use the Hooke's law and SHM formula as found in your own notes, any physics textbook, the data and formula sheets used in exams (available on the exam board's websites) or wikipedia (or any number of other pages found by google)...

and it's always better to start a fresh thread rather than piggybacking onto ancient ones.

Shm

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