Consider the two graphs, shown below, for a block that oscillates back and forth

Question

Consider the two graphs, shown below, for a block that oscillates back and forth on a frictionless surface because it is connected to a spring. The graph on the left shows the block's displacement from equilibrium, as a function of time, for one complete oscillation of the block. The graph on the right shows the elastic potential energy stored in the spring, as a function of time, over the same time period.

(a) What is the spring constant of the spring?

(b) What is the mass of the block?

(c) What is the maximum speed reached by the block as it oscillates?

Consider the two graphs, shown below, for a block that oscillates back and forth on a frictionless surface because it is connected to a spring. The graph on the left shows the block's displacement from equilibrium, as a function of time, for one complete oscillation of the block. The graph on the right shows the elastic potential energy stored in the spring, as a function of time, over the same time period. What is the spring constant of the spring? What is the mass of the block? What is the maximum speed reached by the block as it oscillates?

Explanation / Answer

(a)

For a spring maximum energy = 1/2k*(A)^2 where A is the amplitude.

8 = 1/2*k*(0.4)^2

k = 100 N/m

(b)

Time period = 2 Pi(m/k)^1/2

8 = 2 Pi (m/100)^1/2

m = 162.18 Kg

(c)

Maximum kinetic energy = Maximum potential energy = 8J

1/2*m*v^2 = 8

v = 0.314 m/s

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