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Four springs have been compressed from their
equilibrium position at x = 0 cm. When released, they
will start to oscillate. Rank in order, from highest to
lowest, the maximum speeds of the oscillators.
A. c > b > a = d
B. c > b > a > d
C. d > a > b > c
D. a = d > b > c
E. b > c > a = d
Four springs have been compressed from their
equilibrium position at x = 0 cm. When released, they
will start to oscillate. Rank in order, from highest to
lowest, the maximum speeds of the oscillators.
A. c > b > a = d
B. c > b > a > d
C. d > a > b > c
D. a = d > b > c
E. b > c > a = d
The potential energy stored in the springs gets converted to kinetic energy of the
ball at the equilibrium location. ½kx2 = ½mv2, so |v| = |x|*sqrt(k/m).
This is the position graph
of a mass on a spring.
What can you say about
the velocity and the force
at the instant indicated
by the dotted line?
A. Velocity is positive; force is to the right.
B. Velocity is negative; force is to the left.
C. Velocity is negative; force is to the right.
D. Velocity is zero; force is to the right.
E. Velocity is zero; force is to the left.
This is the position graph
of a mass on a spring.
What can you say about
the velocity and the force
at the instant indicated
by the dotted line?
A. Velocity is positive; force is to the right.
B. Velocity is negative; force is to the left.
C. Velocity is negative; force is to the right.
D. Velocity is zero; force is to the right.
E. Velocity is zero; force is to the left.
The slope of the position graph (or first derivative) gives the velocity. The
slope of the graph of the slope of the position graph (or second derivative)
gives the acceleration. The slope is increasing from negative to positive in the
neighborhood of the point in question, so the acceleration is positive. The sign
of the force matches the sign of the acceleration by Newton’s second law.