Question

A frictionless spring with a 9-kg mass can be held stretched 1 meter beyond its natural length by a force of 40 newtons. If the spring begins at its equiLiBrium position, but a push gives it an initial velocity of 1.5 m/sec, find the position of the mass after t seconds?

Answer 1

The position of the mass after t seconds can be determined using the equations of motion for a mass-spring system.

Step-by-step explanation:

The position of the mass after t seconds can be determined using the equations of motion for a mass-spring system. In this case, since the spring is frictionless, the equation of motion is given by:

x(t) = A * cos(ω * t + φ)

Where x(t) is the position of the mass at time t, A is the amplitude of the motion, ω is the angular frequency, t is the time, and φ is the phase constant.

The amplitude of the motion can be determined using Hooke's Law:

F = k * x

Where F is the force applied to the spring, k is the spring constant, and x is the displacement from the equilibrium position. In this case, the force is 40 N and the mass is 9 kg, so:

40 N = k * 1 m

Therefore, the spring constant is k = 40 N/m.

Using the equation of motion and the given values, you can calculate the position of the mass after t seconds.