Amass m = 1.3 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. the spring has spring constant k = 85 n/m and negligible mass. the mass undergoes simple harmonic motion when placed in vertical motion, with its position given as a function of time by y(t) = a cos(ωt – φ), with the positive y-axis pointing upward. at time t = 0 the mass is observed to be at a distance d = 0.45 m below its equilibrium height with an upward speed of v0 = 5 m/s. a. find the angular frequency of the oscillation in radians per second. b. find the smallest positive value of ϕ in radians. c. calculate the value of a in meters. d. what is the mass's velocity along the y-axis in meters per second at time t1 = 0.15 s? e. what is the magnitude of the mass's maximum acceleration in meters per second squared?

The lights used by mark watley (played by matt damon) during the film the martian seem to be metal halide lamps. metal halide lamps are filled with vaporized mercury and metal-halogen compounds. when an electric current is passed through the lamp, the tube begins to glow a bright white/blue color. if you were to pass this light through a prism to separate the individual light frequencies, you would see a rainbow just as you would if using natural sunlight because of the complexity of the metal halide gas and the vast amount of possible electron transitions. (the study of light in this way is known as spectroscopy and allows astronomers to know exactly what atoms compose distant stars, simply by looking at the light they emit. the spectral lines an atom produces uniquely identifies that atom just like a fingerprint uniquely identifies a person. the momentum equation and energy equation that we have used above can be combined to give the following equation: c = e p where again p is the phonon momentum, e is the photon energy and c is the speed of light. when you divide the photon energy found in #6 by the photon momentum found in #4, do you get the speed of light? (if not, check your work for questions #4 through #6). yes no

Animals respond in various ways to stimuli detected through their senses. some of these responses are stimulated by the presence of danger. which of these animal responses is the best example of a response to an immediate threat? a) a rooster crows every morning at the first sign of light. b) as something approaches an octopus, it shoots a cloud of ink. c) from late fall until spring, bears hibernate to preserve energy. reactivate d) a dog is getting hot in the sunlight, so he moves to a shaded area.

Ahot-air balloonist, rising vertically with a constant speed of 5.00 m/s releases a sandbag at the instant the balloon is 40.0 m above the ground. after it is released, the sandbag encounters no appreciable air drag. compute the velocity of the sandbag at 0.250 s after its release.