Question

A cart of mass m rolls without friction on a level surface, and is attached to a light spring of constant k, the other end of which is attached to a wall. Take the initial position of the cart, where the spring is neither extended nor compressed, to be the origin x = 0 of a coordinate system where positive x values are to the right and positive vectors point to the right. The cart is pushed to the left by a distance d, and then released from rest at time t = 0.

equilibrium ecce عمرو Xډ t = 0 released from rest, d k leelerem X 0

Part 1

The angular frequency ω of the motion of the cart is

a. 0

b. (k / m)^½

c. m / k

d. (m / k)^½

e. k / m

Part 2

At t = 0, the potential energy of the spring is

a. − ½ k d²

b. − k d

c. k d²

d. ½ k d²

e. 0

f. k d

g. − k d²

Part 3

Using a coordinate system where positive vectors points to the right, at t = 0 the force that the spring exerts on the wall is

a. 0

b. k d

c. − k d

d. k d / m

e. − k d / m

f. − k

g. k

Part 4

At t = 0, just after the cart has been released, the acceleration of the cart

a. is zero

b. points to the left

c. points to the right

Part 5

At t = 0, just after the cart has been released, the magnitude of the acceleration of the cart is

a. m k d

b. k / m

c. k d

d. 0

e. k d / m

f. m / (k d)

Part 6

a. The position x(t) of the cart after it is released is

b. d cos(ω t) − d sin(ω t)

c. d sin(ω t)

d. d cos(ω t)

e. −d sin(ω t)

f. − d cos(ω t) + d sin(ω t)

g. −d cos(ω t)

Answer 1

part s. (e) kd/m. past 1 Ans; (b) (m)/2 We know w=a11f we know, a = WA wa ae = A kd part2. at t=0 PE=1 da max displacement. Am&(d) Ind2 past bit ad sinut wave equation is given by = d sinut. Part 3. (d) -kd. F=- kd Part 4. c. points to the right since, change velocity time is towards right. in velo wn