Calculating Velocity and Energy of a Spring Mass System: A Step-by-Step Guide

[bard]

spring mass help--desperate

A 0.35-kg mass at the end of the vibrates 3 times per second with an amplitude of 0.15m. Determine (a)the velocity when it passes the equilibrum point (b)the velocity when it is 0.10m from the equilibrum point(c)the total energy of the system(d)the equation describing the moiton of the mass assuming that at t=0, x was maximum

ok i know that v=sqrtk/m(A^2-x^2)

the velocity would be V=sqrtk/m(0.15^2-0)

V=sqrtk/0.35(0.15^2-0)---other than that I am am stuck can someone help

Thnx

 

[Doc Al]

Find the spring constant k from the frequency f:

f = 1/(2π) √(k/m)

 

[bard]

ok i found K as 1.27 and plugged it back so \

so i got the velocity as 0.28m/s is this right

so then the velocity from 0.1 m from equibium would be

.78m/s

c) total energy of the system would be 1/2KA^2=0.014--dosent make sense

thnx

 

[Doc Al]

I think you messed up the calculations. Do them over.

Here's a practical hint. For a and b, you can just use the value of √(k/m) from the equation I gave. (No need to plug in k and m.) Less chance of calculation error.

 

[bard]

ok i got v=1.59 for part A and v=1.18 for part b

how do i find the total energy of the system?

 

[Doc Al]

Originally posted by bard
ok i got v=1.59 for part A and v=1.18 for part b

how do i find the total energy of the system?

I get different answer for the speeds.

The total energy equals the spring potential energy at maximum compression.