Question

Different mass crates are placed on top of springs of uncompressed length and stiffness. (Figure 1) The crates are released and the springs compress to a length before 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.

A: k=10 N/m L= 5 cm L0=10cm

B: k=20 N/m L=5cm L0=15cm

C: k=15 N/m L= 10cm L0=15cm

D: k=5 N/m L= 5cm L0= 10cm

E: k=10 N/m L=5cm L0= 20cm

F: k=5 N/m L=10cm L0=20cm

Answer 1

As we know that

T = 2π√(m/k)

Also

mg = k*(L0 - L)/2

Therefore

m = k(L0 - L)/2g

Therefore

T = 2π

Therefore

E > F = B > A = D = C