You are Here: Home >< Maths

# M3 Springs watch

1. Question: A particle of mass m is suspended from a fixed point O by a light elastic string of natural length a and modulus of elasticity 4mg. The particle is pulled vertically downwards a distance d from its equilibrium position and released from rest. If the particle just reaches O, find d.

Working:

since the modulus is 4mg, the extension is d and the natural length is a. Since at the highest point all the EPE will be converted into GPE, since the change in height will be a+d. Rearranging into a quadratic we get hence hence or . Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
2. (Original post by Chlorophile)
Question: A particle of mass m is suspended from a fixed point O by a light elastic string of natural length a and modulus of elasticity 4mg. The particle is pulled vertically downwards a distance d from its equilibrium position and released from rest. If the particle just reaches O, find d.

Working:

since the modulus is 4mg, the extension is d and the natural length is a. Since at the highest point all the EPE will be converted into GPE, since the change in height will be a+d. Rearranging into a quadratic we get hence hence or . Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
I have not checked it but a common mistake at this type of problem is that when string has EPE in the equilibrium position too
3. (Original post by TeeEm)
I have not checked it but a common mistake at this type of problem is that when string has EPE in the equilibrium position too
Oh right, that's definitely it. I thought it meant it was pulled a distance d down from its natural length. Thanks!
4. (Original post by Chlorophile)
Oh right, that's definitely it. I thought it meant it was pulled a distance d down from its natural length. Thanks!
no worries

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 22, 2015
Today on TSR

### Tuition fees under review

Would you pay less for a humanities degree?

### Can I get A*s if I start studying now?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE