The intensities of the second and third harmonics are about half that of the fundamental one. Sketch a graph of each wave and a graph of their combination to show the resultant waveform for this violin string.

A1000-kg weather rocket is launched straight up. the rocket motor provides a constant acceleration for 16-s, then the motor stops. the rocket altitude 20-s after launch is 510-m. you can ignore any effects of air resistance. a. what was the rocket’s acceleration during the first 16-s? b. what is the rocket’s speed as it passes through a cloud 5100-m above the ground?

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.

This punnett square shows the cross between two pants. one parent has round seeds (rr). and the other parent has wrinkled seeds (rr) which best describes their offspring as shown in this cross?