Let us consider the spring-mass system shown in the below figure for which the natural frequencies and normal mode shapes should be determined first. Then, you have to determine the resulting free vibration when the system is given an initial displacements x (0) = 5, x, (0) = 1 and initial velocities (0) = x,(0) = 0 k m 2m

A CNC milling machine has a purchase price of £120,000 and it is considered from an accounting standpoint to be depreciated to zero value over a period of 5 years. If the machine is to be used for 2 shifts with each shift working for 37 hours/ week and 45 weeks/ year. What is the machine cost/ hr which must be charged in order to amortise/repay the costs over the 5 year period? To make the calculation simpler, you can assume that over the 5 year period you will be required to pay back 8% interest on the sum borrowed. Express your answer in § / hour rounded up to the nearest penny

The pulley below has a mechanical advantage of 3 and has a load of 300N assume an ideal pulley without friction losses, determine the following: a) what input force (input) do you apply to lift the load of 300 N? B) what is the tension in the 3 lines of the ropes of the pulley on the output side with the load as illustrated in the diagram? C) if the load is lifted to a height of 12 cm, how much rope is pulled on the input side d (in) in the diagram? D) how much work in joules (j) is required to lift the 300 N load 12 cm (0.12m)? E) how much power in watts (w) is required to lift the 300N load a distance of 0.12m in 20 seconds.

Can you please explain how to find the velocity using the methods described? And also why it's done that way? This is from Introduction to robotics mecahnics and controls. Please help ;( !