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## 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 = ω

*x 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 !

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