A simple pendulum with a length of 2.83 m and a mass of 6.84 kg is given an initial speed of 1.36 m/s at its equilibrium position. (a) Assuming it undergoes simple harmonic motion, determine its period. s (b) Determine its total energy. J (c) Determine its maximum angular displacement. (For large v, and/or small l, the small angle approximation may not be good enough here.)

An object thrown vertically upward from the surface of a celestial body at a velocity of 36 m/s reaches a height of sequalsminus0.9tsquaredplus36t meters in t seconds. a. determine the velocity v of the object after t seconds. b. when does the object reach its highest point? c. what is the height of the object at the highest point? d. when does the object strike the ground? e. with what velocity does the object strike the ground? f. on what intervals is the speed increasing?

Hydrogen atoms are excited by a laser to the =4n=4 state and then allowed to emit. what is the maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system? 8 6 2 7 4 5 1 3 calculate the wavelength of the 4⟶14⟶1 transition. =λ=

State the following: boyle's law and charle's law