1. An object of mass M = 2, 0 kg is attached to a spring of elastic constant k = 50 N/m which is compressed a distance d = 20 cm and then released from rest, Fig. 1(a). (a) Find the velocity of the object when it has passed from the point where the spring is relaxed and the spring is stretched a distance of 10 cm. Assume that the mass is moving horizontally, on a frictionless surface. (b) Show, from Hooke's law, that the function x(t) = Acos(ωt + φ) is a possible solution for the motion of this block. Determine the constants of this function (A, ω, and φ) and use it to find out how long it takes the mass to go from the starting point with the spring compressed by 20 cm to the point where the spring is stretched by 10 cm. (c) Write an equation for the velocity as a function of time, using the same denition of t = 0 as in part (b). Use this equation to find the vel
1. An object of mass M = 2, 0 kg is attached to a spring of elastic constant k = 50 N/m which is compressed
a distance d = 20 cm and then released from rest, Fig. 1(a). (a) Find the velocity of the object when it
has passed from the point where the spring is relaxed and the spring is stretched a distance of 10 cm. Assume that the mass
is moving horizontally, on a frictionless surface. (b) Show, from Hooke's law, that the function
x(t) = Acos(ωt + φ) is a possible solution for the motion of this block. Determine the constants of this function
(A, ω, and φ) and use it to find out how long it takes the mass to go from the starting point with the spring compressed by
20 cm to the point where the spring is stretched by 10 cm. (c) Write an equation for the velocity as a function of
time, using the same denition of t = 0 as in part (b). Use this equation to find the velocity (magnitude
and direction) when time is t = 3T/4 where T is the period of motion of the mass in the spring.
Step by step
Solved in 8 steps
