Problem

The mass m shown in the figure is displaced a distance x to the right from equilibrium pos...

The mass m shown in the figure is displaced a distance x to the right from equilibrium position.

a) What is the net force acting on the mass, and what is the effective spring constant?

b) If k1 = 100. N/m and k2 = 200. N/m, what will the frequency of the oscillation be when the mass is released?

c) If x = 0.100 m, what is the total energy of the mass spring system after the mass is released, and what is the maximum velocity of the mass?

Step-by-Step Solution

Solution 1

Step #1 of 7

THINK:

Frequency of spring mass system depends on the spring constant and mass. Once the mass has been displaced to the right and at the moment the mass is released, there will be two forces acting on it. The forces are due to springs 1 and 2.

Step #2 of 7

RESEARCH:

When the two springs are connected in parallel combination, then the resultant force constant is.

Step #3 of 7

SIMPLIFY:

Restoring force acting on the left spring is

Restoring force acting on the right spring is

Net force acting on the mass is

Frequency of the oscillation is

Total energy of oscillator is

Step #4 of 7

CALUCULATE:

(a) Net force acting on the mass is

Effective spring constant is

Step #5 of 7

(b) Frequency of the oscillation when the mass is released is

Step #6 of 7

Step #7 of 7

The maximum velocity of the mass is obtained as follows.

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Solutions For Problems in Chapter 14

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