a mass m is subject to a resistive force -bv but no springlike restoring force. (a) show that its displacement as a function of time is of the form where γ = b/m. (b) at t = 0 the mass is at rest at x = o. at this instant a driving force f = fo cos ar is switched on. find the values of a and δ in the steady-state solution x a cos(wt-5). (c) write down the general solution [the sum of parts (a) and (b)] and find the values of c and vo from the conditions that x -0 and dx/dt = 0 at t 0. sketch x as a function of 1.

Mike walks 100 meter north, then walks 30 meters south. after this, he walks another 10 meters north. what is the magnitude of his total displacement during this walk,in meters?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Light traveling in a medium with a refractive index 1.19 is incident on a plate of another medium with index of refraction 1.79. at what angle of incidence is the reflected light fully polarized?