A block of mass m = 3kg is attached to a light spring with a spring constant k and moves in simple harmonic motion on a frictionless horizontal surface. Initially the spring is compressed to x, = -0.1 m from its equilibrium position and is given an initial velocity vo in the negative x-direction, as shown in the figure below. The maximum speed reached by the block is vmax = V2 m/s. The block's period of oscil- lation is T= 0.889s. 4) The phase constant o in x(t) = A cos(@t + q) is: hmmm a. + rad Equilibrium b. + rad 3. rad 3 с. -- - rad wwm d. =- 0.1m

A simple pendulum of lengthL=0.972m with a bob of mass m=45.8g is pulled aside untilthe bob is at a height L/4 above its equilibrium position. Thebob is then released. Find the speed of the bob as it passesthrough a point where its height is L/7 above its equilibriumposition. What is the angle the pendulum makes with thevertical at this point?

A spring-loaded toy gun is used to shoot a ball of mass m = 1.50 kg straight up in the air, as shown in (Figure 1). The spring has spring constant k = 667 N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y = 0 and then released, the ball reaches a maximum height hmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis. Figure hmax y=0 ☹ 1 of 1 Part B Find vm the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y = 0). ▸ View Available Hint(s) Um = Submit Part C v A Templates Symbols undo redo reset keyboard shortcuts help Find the maximum height hmaxof the ball. Express your answer numerically, in meters. ▸ View Available Hint(s) hmaxe Submit ▾ Part D Templates Symbols undo redo reset keyboard shortcuts help Submit m/s Which of the…

A cube of a mass m=0.37 kg is set against a spring with a spring constant of k1=656 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2=181N/m. The cube is not connected to the first spring and may slide freely. I found (a) and (b). I just need help with (c). a). How far d2, in meters, will the second spring compress when thee cube runs into it? 0.19 m. (answer) b). How fast v, in meters per second, will the cube be moving when it strikes the second spring? 4.21 m/s (answer) c). Now assume friction is present on the surface in between the ends of the springs at their equilibrium lengths, and the coefficient of kinetic friction is uk=0.5. If the distance between the springs is x=1m, how far d2, in meters, will the second spring now compress?