Mass on a Spring: Determine Periodic Time, Frequency & Acceleration

[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