Question

Cart 1. Make two pictures of the oscillating cart (1) one at its equilibrium position and (2) one at some other position and time while it is oscillating. On your pictures, show the direction of the velocity and acceleration of the cart and the forces on the cart. 2. Draw a force diagram of the oscillating cart when it is at a position away from its equilibrium position. Label the forces. 3. Write down an equation for the total force on the cart in terms of the two spring constants and its disp lacement from the equilibrium position 4. Now imagine that only one spring was attached to the cart, but it exerted the same force at the same disp lacement as the two-spring system. How would the motion of these two systems compare? What is the relationship between the spring constant of the single spring system and the two for the two-spring system? 5. Write down an equation for the frequency of the imaginary one spring system. How does it compare with the frequency of the two-spring system?

Answer 1

Net force is zero rightarrow v notequalto 0 it may be in forward or in backward direction rightarrow a = 0 because at equilibrium net force on the cost is zero rightarrow in spring 1 f_1 acts inwards and f_2 to spring 2 acts outward direction rightarrow net force is non zero and acceleration of the block will be in negative direction forces on cost force diagram extension in spring x_1 = compression in spring x_2 implies x_1 = x_2 = x implies f_1 = k_1 x f_2 = k_2 x net force on cost = f = f_1 + f_2 f = (k_1 + k_2)x here x = displacement from eqn position if k_1 = k_2 = k implies f = (2k)x

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