A block with m = 300 grams oscillates at the end of a linear spring with k = 6.5 N/m. (assume this is a top-down view and the block is sliding on a frinctionless surface; neglect gravity)

a) what is the period of the block's motion in seconds

b) if the blovk's max acceleration is 2 m/s^2, what is the amplitude of the motion (m)

a) T=1.35s

b) amplitude = 0.0923m

Explanation:

m=300 gr

k=6.5 N/m

first we need to get the angular frequency of the motion

so we have that

ω = √ (k/m)

in this case motion is a simple harmonic so the period is defined by:

T = 2π / ω

T = 2π / √ (k/m)

replacing the variables ...

T = 2π / √ (6.5/0.3)

T=1.35s (period of the block's motion)

and ...

α max = | ω²r max |

2 = (2π/1.35) ² * r max

r max = 0.0923m