Suppose that a car weighing 2000 pounds is supported by four shock absorbers each shock absorber has a spring constant of 6250 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 25000 lbs/foot. 1. assume no damping and determine the period of oscillation of the vertical motion of the car. hint: g 32 f/sec2 t314 2. after 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. what were the initial seconds. conditions? 2 0.4871 ft, and yt y(o,-0100x 0.487 ft. and y(0)- x ft/sec. 3. now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of - 6.93 ib-sec/ft times the vertical velocity of the car body. find the displacement y(t) from equilibrium if y(0)-0 ft and y( ft/sec. y(t)

Herbivores, carnivores, and omnivores are all types a. decomposers b. producers c. consumers d. biomes

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 ⇒

When the magnetic domains in a material can be aligned, but eventually drift out of alignment, the material is