# SHM(mass suspended vertically on spring)

## Homework Statement

An object is hung on the end of a vertical spring and is released from rest with the spring unstressed. If the object falls 3.42 cm before coming to rest, find the period of the resulting oscillatory motion.

## The Attempt at a Solution

This was a homework question given and the answer is in the back of the book and it says
T = .262 seconds. Now i have no clue how they got this because I thought that the period was related to the spring constant and the mass but not to the amplitude so how can we find T if neither k nor m is given?

## Answers and Replies

cepheid
Staff Emeritus
Science Advisor
Gold Member
so how can we find T if neither k nor m is given?

Hi nrweis, welcome to PF!

You can deduce something about them from the restoring force that is required to balance the object's weight.

LowlyPion
Homework Helper
Welcome to PF.

You don't necessarily need m and k, because don't you also know that

a(t) = ω2*x(t)

Won't a(t) = 9.8 at x/2 from the dead weight equilibrium point, which is at the peak of its oscillation?

Since ω = 2πf = 2π/T ...

Ok I thought about it for a while and thought I was on the right track but still got it wrong. This is what i did:

F=k∆x
mg=k∆x

√(g/∆x)= √(k/m)=ω=2π(1/T)

√(g/∆x)= 2π(1/T)

T=2π√(∆x/g)

and I got like .37 seconds.
Was I on the right track?

now I'm all confused. I was thinking that delta x was the amplitude

ok I just misunderstood the question. When I divided the 3.42 cm by 2 and reentered it to the formula I got the right answer. Thanks guys.

LowlyPion
Homework Helper
now I'm all confused. I was thinking that delta x was the amplitude

Yes. Δx is the amplitude, but the x-position function which expresses x as a function of time is only x/2 distant from the mid point.

Congrats on figuring it out.