Using hookes law to find impulse

AI Thread Summary
To find the impulse delivered to the block during the first two seconds of oscillation, the force versus time graph must be analyzed. The impulse can be calculated using the formula F*Δt, but since the force varies with time, integration of the force function over the time interval is necessary. The force function is likely sinusoidal, based on the oscillation characteristics provided. The key steps involve determining the force function and integrating it from 0 to 2 seconds to obtain the impulse. This approach will yield the desired result for the impulse experienced by the block.
captainhooke1
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Homework Statement


You are given a FORCE versus TIME graph, which shows oscillations with:

A= 4N at the max points
period is 4s
spring constant (k)= 12.3 N/m
mass of block exhibiting oscillation is 4.9 kg


How do you find the IMPULSE delivered to the block during the 1st 2 seconds of oscillation?

2. Homework Equations :
impulse=Δp
E=kx
x(t)= Acos(wt)
w=2∏f
W=deltaEk or F(D)



The Attempt at a Solution


x(t)=Acos(wt)

x(0)=4cos0=4N
x(2)=4N

I don't know how to connect this information
 
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Welcome to PF, Captain!
Do you have the graph? It depends where it starts - is F=0 at time zero or what?
The usual impulse formula is F*Δt. Your F varies with time; can you integrate F*dt over the Δt?
 
Find the function F that defines force (it is a sine or cosine, from what you told). Integrate it over the time interval from 0 to 2 seconds.
 

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