The 20-kg block is subjected to the action of the harmonic force F = (90 cos 6t) N, where t is in seconds. (Figure 1) Figure k-400 N/m w k= 400 N/m 20 kg F-90 cos 6 D c=125 N-s/m < 1 of 1 ▼ Part A Write the equation which describes the steady-state motion. Express your answer in terms of t. Express your answer using three significant figures. Express the phase in radians and the final result in meters. Submit Provide Feedback AΣ vec Request Answer ? m Next >

4. A spring with stiffness constant k = 2000 N/m attached to a platform launched a mass of 2kg vertically in the air to some maximum height (measured from the equilibrium point of the spring). The spring was compressed by 0.3 meters before launch. Due to internal friction of the spring, 10 Joules of energy was lost as the spring expanded. How fast was the mass travelling when it was at half of its maximum height? You must use g= 10m/s? for this problem or you will actually find it much more difficult to calculate. Hint: First solve the problem of finding what the maximum height is and then solve the problem of finding the speed at half of that height.

Damian’s car weighs 2000kg. The spring has a natural unstretched length of 2m and a spring constant of k = 80000N/m.  Hooke's law can be written as T = kd. Where T is the tension force in newtons, k is the spring constant and d is the length in metres. Let x(t) be the position of the front of Damian’s car and let y(t) be the position of the back of Eva’s 4WD. We will assume that the position of Eva’s car is a known function of time. Q1 a) Create a sketch of the positions of the vehicles similar to the one given and add the positions x and y. b) What is the extension of the spring in terms of x(t) and y(t)? Be careful to take into account that the unstretched length of the spring is 2m.

A used battery was brought to the workshop and the technician noticed that it had 1 litre of distilled water in it but was fully discharged. The specs sheet for this type of battery states that it is fully charged when the change in distilled water to the change in charge equals to the difference between twice the amount of charge and the actual amount of distilled water existing in the battery For the used battery, derive the differential equation and state the initial condition for the range x= 0(0.2)1.0, then obtain a numerical solution for this equation using Euler’s method.