A horizontal mass–spring system consists of a block of mass attached to a spring of…

PHYSICS · Multi-part · CBSE · Physics · Oscillations · Oscillations

Problem

A horizontal mass–spring system consists of a block of mass

0.50\,\text{kg}

attached to a spring of force constant

80\,\text{N\,m}^{-1}

. A small electric motor can drive the block with an adjustable driving frequency. (a) Calculate the natural angular frequency

\omega_0

and the corresponding natural frequency

f_0

of the block–spring system. (b) The motor can be set to any of the following angular frequencies:

6.0\,\text{rad\,s}^{-1}

12.5\,\text{rad\,s}^{-1}

and

40.0\,\text{rad\,s}^{-1}

. Identify which setting will produce resonance. (c) For the setting chosen in part (b), determine the driving period

T

. (d) If an identical second block is rigidly attached to the first one so that the total oscillating mass becomes

1.00\,\text{kg}

while the same spring is retained, calculate the new natural frequency that will now be required for resonance.