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Simple Harmonic Motion Mass on a Spring Ranking

Different mass crates are placed on top of springs of uncompressed length L_0 and stiffness k. The crates are released and the springs compress to a length Lbefore bringing the crates back up to their original positions.

Rank the time required for the crates to return to their initial positions from largest to smallest.

1 )
k= 10 n/m
L= 5 cm
L_0= 10 cm

2)
k= 5 n/m
L= 10 cm
L_0= 20 cm

3)
k= 20 n/m
L= 5 cm
L_0= 15 cm

4)
k= 15 n/m
L= 10 cm
L_0= 15 cm

5)
k= 10 n/m
L= 5 cm
L_0= 20 cm

6)
k= 5 n/m
L= 5 cm
L_0= 10 cm

Please explain equation used.Thank you!!

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Homework Answers

Answer #1

As we know that

T = 2π√(m/k)

Also

mg = k*(L0 - L)/2

Therefore

m = k(L0 - L)/2g

Therefore

T = 2π28

Therefore

E > F = B > A = D = C

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