Amass of 5 kg stretches a spring 20 cm. the mass is acted on by an external force of 10 sin t 6 n (newtons) and moves in a medium that imparts a viscous force of 6 n when the speed of the mass is 3 cm/s. if the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass. (use g = 9.8 m/s2 for the acceleration due to gravity. let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. use up for u' and upp for u''.

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 ⇒

Write the function getkthdigit(n, k) that takes a possibly-negative int n and a non-negative int k, and returns the kth digit of n, starting from 0, counting from the right

Which of these has some mechanical energy? a. an atom b. heat inside earth c. a book on a shelf d. the fire from a lit match