How Long Does It Take for a Mass to Oscillate Between Two Points on a Spring?

[shasanni]

Homework Statement

A vertical spring stretches 9.6 cm when a 1.3kg block is hung from its end.This block is then displaced an additional 5.0 cm downward and released from rest. Calculate the time it takes the object to go from a point 0.025 m below its equilibrium position to a point 0.025 m above it.

Homework Equations

X1= Acos(Wt1)
X2=Acos(Wt2)
A represents the amplitude, which is 0.05 m. The W represents the angular frequency, which is 10.1

The Attempt at a Solution

This is how I sent things up:
0.025=0.05cos(10.1t1)
-0.025=0.05cos(10.1t2)
and then I would have subtracted the two times, but I am not getting the correct values for t1 and t2. What am I doing wrong??
Btw, the answer is supposed to be 0.1s. T2 is 0.2s and T1 is 0.1s. ?

 

[ehild]

What did you get for t1 and t2?

ehild

 

[shasanni]

This are the values I get:
t1= 0.507
t2=-.0507

 

[ehild]

cos(ωt1)=0.5 corresponds to ωt1=π/3.
cos(ωt2)=-0.5 corresponds to ωt2=π-π/3.
What are t1 and t2 then?

ehild

 

[shasanni]

i think I know what the issue is. I have been using radians, not degrees!
t1 should 0.1 seconds and t2 should be 0.2 s. The change in time should be 0.1 seconds, which is the answer.

 

[ehild]

Well done! take care of radians and degrees in the future.

ehild