A 140 g mass is connected to a light spring of force constant 5 N/m that is free to oscillate on a horizontal, frictionless track. The mass is displaced 3 cm from the equilibrium point and released from rest.

(A) Find the period of its motion.
(B) Determine the maximum speed of the block.
(C) What is the maximum acceleration of the block?
(D) Express the position, velocity, and acceleration as functions of time in SI units.

Explanation:

mass attached m = .14 kg

force constant k = 5N / m

displacement

= amplitude of oscillation

A = .03 m

A ) period of motion =

= 2 x 3.14

T = 1.05 s

B ) maximum speed of block = angular velocity x amplitude

= (2π /T)  x A

= (2 x 3.14 x .03) / 1.05

= .1794 m / s

17.94 cm /s

C )

maximum acceleration = angular velocity² x amplitude

= (2π /T)² x A

= (2π /1.05)² x .03

= 1.073 m / s²

D )

position

S = A cos ωt , ω is angular velocity

S = .03 cos(2πt /T)

= .03 cos 5.98 t

v =ω A sin(2πt /T)

= 5.98 x .03 sin5.98t

= .1794 sin5.98t

acceleration = ω²A sin5.98t

= 1.073 sin5.98t

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

statement #3 on andre"s list is false.