A string of length 3m and total mass of 12g is under a tension of 160N. A transverse harmonic wave with wavelength 25cm and amplitude 2cm travels to the right along the string. It is observed that the displacement at x=0 at t=0 is 0.87cm. a) What is the wave?
b) Wrote the wave function, y(x, t)
c) Find the particle velocity at position x=0 at time t=10s. What is the maximum particle velocity?​

The density of a liquid could be found by using

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.

Immediately upon reaching its lowest point, a falling pendulum bob has its greatest amount of energy, which is the initial amount of potential energy. a. heat; less than b. heat; more than c. kinetic; less than d. kinetic; more than