Question

A scientist is testing the seismometer in his lab and has created an apparatus that mimics the motion of the earthquake felt in part (a) by attaching the test mass to a spring. If the test mass weighs 13 N, what should be the spring constant of the spring the scientist use to simulate the relative motion of the test mass and the ground from part (a)?

Answer 1

Complete Question

The complete question is shown on the first uploaded image  

Answer:

a

 $a_{max} = 0.00246 \ m/s^2$

b

   $k =722.2 \ N/m$

Explanation:

From the question we are told that

     The  amplitude is $A = 1.8 \ cm = 0.018 \ m$

     The period is $T = 17 \ s$

    The test weight is  $W = 13 \ N$

Generally the radial acceleration is mathematically represented as

        $a = w^2 r$

at maximum angular acceleration

       $r = A$

So  

       $a_{max} = w^2 A$

Now $w$ is the angular velocity which is mathematically represented as

      $w = \frac{2 * \pi }{T}$

Therefore

       $a_{max} = [\frac{2 * \pi}{T} ]^2 * A$

substituting values

       $a_{max} = [\frac{2 * 3.142}{17} ]^2 * 0.018$

       $a_{max} = 0.00246 \ m/s^2$

Generally this test weight is mathematically represented as

     $W = k * A$

Where k is the spring constant

Therefore

        $k = \frac{W}{A}$

substituting values        

      $k = \frac{13}{0.018}$

     $k =722.2 \ N/m$