Simple Harmonic Motion Quiz B
D
E
1. In the diagram to the right, a block is
attached to a Hookean spring. The spring
is neither stretched nor compressed at
position C. Assume that frictional effects
are negligible. The velocity vs. time
graph below represents the motion of the O-
block as it oscillates between positions A
and E. Fill in the boxes with the correct
0
positions corresponding to the graph shown. On the axes indicated, sketch the corresponding
position, acceleration, force, kinetic energy, elastic energy, and total energy vs. time graphs.
U
velocity
time
time
acceleration position
time

How would doubling the made of an object change the objects potential energy

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.

Dao makes a table to identify the variables used in the equations for centripetal acceleration. what quantities belong in cells x and y?