I would really appreciate some help on this problem. I am stuck, so a step by st

Question

I would really appreciate some help on this problem. I am stuck, so a step by step would be greatly appreciated. Question is from Mastering Physics and allows no example problems.

(Figure 1) shows two springs, each with spring constant 17 N/m , connecting a 2.9 kg block to two walls. The block slides on a frictionless surface. If the block is displaced from equilibrium, it will undergo simple harmonic motion. The block is displaced 1.0 cm from equilibrium.

Part A

What is the magnitude of the restoring force?

Part B

What is the effective spring constant of the two springs working together?What is the effective spring constant of the two springs working together?

Part C

If the mass is released, it will oscillate. What is the frequency?

Thanks in advance

Explanation / Answer

spring force=spring constant*displacement of the spring

if spring is compressed, the force will be in opposite direction to the compression

if spring is stretched, the force direction will be opposite to direction of stretching.

so here as one spring is stretched and other is compressed,

both the spring forces are aligned in same direction

hence the equivalent spring constant=addition of spring constant of both the springs

=17+17=34 N/m

part 1:

restoration force=equivalent spring constant*displacement=34*0.01=0.34 N

part 2:
effective spring constant=34 N/m

part 3:

frequency of oscillation=sqrt(spring constant/mass)

=sqrt(34/2.9)=3.4241 rad/sec

in units of Hz, frequency=3.4241/(2*pi)=0.54495 Hz

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects