A 48-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 3 m. The mass is in a medium that exerts a viscous resistance of 912 N when the mass has a velocity of 3 m/sec. Assume the mass is given an initial velocity of 10 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k=
b) Determine the damping coeffient 7. 7=
c) If the initial value problem for y(t), where y(t) denotes the displacement (in meters) of the mass from its equilibrium rest position, can be written in the form my'' + yy' + ky O where y(0) = yo and y'(0) = y'. what are the values of yo and y'o? Yo = yo
d) Solve it only far enough to describe the motion of the system with the terminology of this course. The system is e) What value of the damping coefficient y is required for the system to be critically damped? No decimals. Use "sqrt(foo)", without quotes, if you need the square root of foo. 7=

Bernie drove home from a vacation in 1.5 hours. he traveled a total distance of 60 miles. what was his average speed in miles per hour? a. 60 mph b. 90 mph c. 40 mph d. 55mph

When a spring is compressed, the energy changes from kinetic to potential. which best describes what is causing this change? work power gravitational energy chemical energy

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 ⇒