Ablock is attached to a horizontal spring and oscillates back and forth on a frictionless horizontal surface at a frequency of 4.42 hz. the amplitude of the motion is 8.26 x 10-2 m. at the point where the block has its maximum speed, it suddenly splits into two identical parts, only one part remaining attached to the spring.
(a) what is the amplitude and
(b) the frequency of the simple harmonic motion that exists after the block splits?



Amplitude = 0.058m

Frequency = 6.25Hz

Explanation:

Given

Amplitude (A) = 8.26 x 10-2 m

Frequency (f) = 4.42Hz

Conversation of energy before split

½mv² = ½KA²

Make A the subject of formula

A =

Conversation of energy after split

½(m/2)V'² = ½(m/2)V² = ½KA'²

½(m/2)V² = ½KA'²

Make A the subject of formula

First divide both sides by ½

(m/2)V² = KA'²

Divide both sides by K

V² = A'²

= A'

Substitute for A in the above equation

A' = A/√2

A' = 8.26 x 10^-2/√2

A' = 0.05840702012600882

Amplitude after split = 0.058 (Approximated)

Frequency (f') = f√2

f' = 4.42√2

f' = 6.25082394568908011

Frequency after split = 6.25Hz (approximated)

1/0.14nm = 10^10/1.4 a lot

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.