# Mass on a spring

Thermoman

## Homework Statement

A spring has a stiffness of 30 KN/m and supports a mass of 8 kg. The mass is pulled so that the spring t extends by amplitude of 10 mm and its released so that it produces linear oscillations .

## Homework Equations

(i) Determine the periodic time,circular frequency,and the natural frequency f.
(ii) Calculate the maximum velocity of the mass.(iii) Calculate the maximum acceleration of the mass.

## The Attempt at a Solution

Periodic time;

T = 1/f = (1 / 9.75) = 0.10260s

Circular frequency;

W= √ k / M w = √ 30000 / 8 = 61.24 rad/s

Natural frequency;

F = w / 2 π = 61.24 / (2π) = 9.75Hz

Displacenent . [/B]10 cos X (61.24 X 0.10260) = - 5.27 mm
Which equations do I use ? Velocity = ωx sin ωt Or max velocity = x cos ωt =0
Acceleration= ω^2 x sin ωt Or max acceleration= x cos ωt

If I am correct with displacement , it does not equal zero.Which is throwing me !

melthengylf
i don't think those equations of max velpcity have any sense. if they are maximum, why would tgey depend on time??

Thermoman
The question is written out word for word. There have been other problems with questions on this assignment and the one on thermodynamics before it ! Its an online BTEC. Are you saying the question it self is incorrectly written (others have been). And i struggled with them too.
Should i just treat it as velocity ? And acceleration , Leaving Max out of it ?

melthengylf
look, max velocity is $\omega xmax$. max acceleration is $\omega^2 xmax$. you shouldn't have any "time" involved.

Thermoman
Those are the equations used in the course examples ? So you're saying the equations I put up are incorrect to find max acc and max Vel ?

melthengylf
Those are the equations used in the course examples ? So you're saying the equations I put up are incorrect to find max acc and max Vel ?
yes, those equations are wrong. the correct equations are those that I gave you. it is easy to do it yourself, just derive with respect to time and rember that sine and cosine are between 1 and -1. it is crucial to understand this that the maximum velocity or acceleration can't involve time

Thermoman
Thank you melthengylf...No wonder I am bamboozed