A 50-cm-long spring is suspended from the ceiling. A 330g mass is connected to the end and held at rest with the spring unstretched. The mass is released and falls, stretching the spring by 28cm before coming to rest at its lowest point. It then continues to oscillate vertically.

A. What is the spring constant?

B. What is the amplitude of the oscillation?

C. What is the frequency of the oscillation?

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

Assume that a person skiing high in the mountains at an altitude of h = 15100 ft takes in the same volume of air with each breath as she does while walking at sea level. determine the ratio of the mass of oxygen inhaled for each breath at this high altitude compared to that at sea level. assume that the air composition (i.e. % of air that is oxygen) is the same at sea level as it is at 15100 ft.

Consider the growth of a 20-nm-diameter silicon nanowire onto a silicon wafer. the temperature of the wafer surface is maintained at 2400 k. assume the thermal conductivity of the silicon nanowire is 20 wm-1k-1 and all its surfaces including the tip are subjected to convection heat transfer with the coefficient h = 1×105 wm-2k-1 and t∞ = 8000 k. when the nanowire grows to l = 300 nm, what is the temperature of the nanowire tip (t (x =