A mass m attached to a spring of constant k is oscillating on a frictionless surface. A second mass of mass m is dropped on top of the first at the moment the spring is extended to the end (x = A). Which of the following is true?
A. The maximum velocity does not change.
B. The amplitude of the oscillation A decreases.
C. The frequency of oscillations f does not change.
D. The frequency of oscillations f increases.
E. The period of oscillation increases.

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.

Suppose you increase your walking speed from 7 m/s to 13 m/s in a period of 2 s. what is your acceleration?

Distinguish between linear momentum and angular momentum