Luke is trying to catch a pesky animal that keeps eating vegetables from his gar

Question

Luke is trying to catch a pesky animal that keeps eating vegetables from his garden. He is building a trap and needs to use a spring to close the door to his trap. He has a spring in his garage and he wants to determine the spring constant of the spring. To do this, he hangs the spring from the ceiling and measures that it is 21.9 cm long. Then he hangs a 1.10-kg brick on the end of the spring and it stretches to 36.9 cm.

(a) What is the spring constant of the spring?
N/m

(b) Luke now pulls the brick 4.8 cm from the equilibrium position to watch it oscillate. What is the maximum speed of the brick?
m/s

(c) When the displacement is 2.4 cm from the equilibrium position, what is the speed of the brick?
m/s

(d) How long will it take for the brick to oscillate five times?
s

Explanation / Answer

Given that

mass m=1.1 kg

distance x1=21.9 cm

distance x2=36.9 cm

basing on the concept of oscillations

now we find the spring constant

F=k[x2-X1]

1.1*9.8=K[0.369-0.219]

spring constant K=71.9 N/m

now we find the maximum speed of block at distance 4.8 cm

the maximum speed Vmax=WA=[K/m]^1/2*x=[71.9/1.1]^1/2*0.048

                                    =0.4 m/s

now we speed at a distance 2.4 cm

speed V=[71.9/1.1]^1/2*0.024=0.2 m/s

now we find the ttime period oscilations takes 5 times

time period for one oscillation T=2*3.14*[m/k]^1/2=2*3.14*[1.1/71.9]^1/2=0.78 sec

the time period for 5 time increases =5*0.78=3.9 sec

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