Mechanics | Relativity Answers

Write down the differential equation for a damped harmonic oscillator. What is the basis of representing the damping force in terms of velocity? Show that the average energy of a weakly damped oscillator is given by:
< E > = E0 exp (- 2bt)

(a)Show that the average kinetic energy associated with SHM is .1/4ka²
b) A rubber pad acts as an elastic spring. When a mass of 200 g is placed on it, a compression of 2.0 cm is produced. The spring-mass system begins to oscillate when the mass is gently tapped downwards. Calculate the frequency of oscillation.

A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in Figure 5.10a. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable, and will break if the tension in them exceeds 100 N. Will the traffic light remain hanging in this situation, or will one of the cables break

A car of mass m is on an icy driveway inclined at an angle θ as in Figures below. Find the acceleration of the car, assuming that the driveway is frictionles

a truck is traveling on a straight line on ground level and is accelerating uniformly with an acceleration of magnitude (a). a rope is tied to a bucket of mass (m), the bucket tosses widely when the truck starte to accelerate but later on displaces at a fixed position at a fixed distance behind the truck and the rope hanging straight at a fixed angle; find the angle at which the rope will settle.express your answers in terms of m, g and a

Consider the state of stress in a bar subject to compression in the axial direction. Lateral expansion is restrained to half the amount it would ordinarily be if the lateral faces were load free. Find the effective modulus of elasticity.

A light-rail commuter train accelerates at a rate of 1.35 m/s2. How long (in s) does it take to reach its top speed of 80.0 km/h, starting from rest?

If you drop an aspirin from rest and it takes 0.35 seconds to hit the table, how high above the table was the aspirin when it was released?

a.
1.72 m

b.
1.2 m

c.
0.6 m

d.
3.43 m

A bullet is fired vertically upward with an initial velocity of 98m/s from the top of a building 100m high. Find
1. The maximum height reached above the ground
2. The total time before reaching the ground
3. The velocity on landing

(Question in statics of objects)
A cantilever horizontal beam ABCD of negligible weight is completely fixed at D to a wall.It is subjected to a uniform distributed load on the part AB of intensity q=qo kN/m ,and a linearly distributed load on the part BCD of intensity q=qo kN/M at point B and q=0 at D.In addition, the beam is also subjected to a force F1=qo kN at A , a force F2 =2qo kN at B and a moment couple M1=qo/3 kN.m at B ,and a Force F3=2qo kN and a moment couple M2=2qo kN.m at C.
(Note the loads are directed downward, F3 is directed downward, while the others are upward, M1-M2 are clockwise,AB=BC=CD=2m)
It is required to determine the equations of the internal actions on the beams part ABC and represent them graphically (SFD & BMD)