A string has a mass of 13.7 g. The string is stretched with a force of 8.21 N, giving it a length of 1.91 m. Then, the string vibrates transversely at precisely the frequency that corresponds to its fourth normal mode; that is, at its fourth harmonic. What is the wavelength of the standing wave created in the string

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.

True or false when elements combine to form a mixture, the resulting chemical properties may be very different from those of the elements that make it.

What is the energy of a photon of ultraviolet radiation with a frequency of 4.4 × 1015 hz? planck’s constant is 6.63 × 10–34