please refer to the image and answer both questions

2. (25 points) In the figure below is shown an elastic string of beads that is being driven by a piston to produce a sinusoidal wave. It is shown at a time / =0 and moves to the right once the clock starts running Use the x-y coordinate system shown by the dotted lines and the distance scale shown by the rulers. 30 10 em 2.1 The rod driving the wave goes through a single up-down-up cycle in a time of 0.2 seconds. The genera equation for the displacement y of the bead at position x at time t, is y(x,t) = A [sin or cos] { 2n (*/2 - '/T)} Determine the numerical details below for this wave's equation from the diagram and cycle time provided above (2 pts each, 8 pts total): (a) Amplitude A (b) Wavelength 2 (c) Period T (d) Given the position of the wave at t = 0, should this equation use sin or cos? 2.2 Calculate with what speed vo the wave will travel down the string. (4 pts) 2.3 How long will it take the crest/peak at x = 10cm to reach x = 50cm? (4 pts) 2.4 Given that the vertical (y) speed of any bead at some instant is v(x,t) = (/dx ) vo, where vo is wave speed, determine the maximum up-down speed Vmax of the any bead in this wave. (7 pts)5. (25 points) A cart is attached to a wall by a spring. Its position is measured by a sonic ranger, but the origin has been shifted so that it is at its equilibrium point when x = 0. The friction in the wheels, the damping in the observations. spring, and air resistance can all be ignored for the few seconds of these x(t) = A sin (wt) T = 2mm/k U= 1/2 /x Eo = KE + U = Umax = KEmax KE = 1/2 mv The cart is started oscillating and then the sonic ranger is started. The resulting position graph is shown below . 015 (sec) 5.1 Indicate the direction of the velocity of the cart and the acceleration that it is feeling at the times below. Use "+" or "_" to indicate the positive direction or to the right, "-" or " " to indicate the negative direction or the the left, and "0" to indicate zero. (8 pts) t = 0.1s direction a direction t = 0.2s direction a direction t = 0.4s direction a direction t = 0.55s direction a direction 5.2 Find the period 7, and, given that the mass of the cart is 250 grams, find the spring constant k. (6 pts) 5.3 Find the total energy E. in the oscillating cart-spring system in Joules. (6 pts) 5.4 Find the maximum speed Vmax of the cart during the oscillation in m/s. (5 pts)