Abody of mass 5 gm is executing s. h.m. about a point with amplitude 10 cm. its maximum velocity is 100 cm/sec. its velocity will be 50 cm/sec at a distance.

a. 5
b. 5√2
c. 5√3
d. 10√2

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.

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Which situation will produce the greatest change of momentum