question_answer 9)

A spring of force constant \[1200\,N{{m}^{-1}}\] is mounted on a horizontal table as shown in Fig. 10 (NCT).3. A mass of 3.0 kg is attached to the free end of the spring, pulled side ways to a distance of 2.0 cm and released. Determine (a) the frequency of osculation of the mass. (b) the maximum acceleration of the mass. (c) the maximum speed of the mass.

Answer:

Here, \[k=1200\,\,N{{m}^{-1}};\] \[m=3.0\,kg,\] \[a=2.0\,cm=0.02\,m\] (a) Frequency, \[\text{N}{{\text{m}}^{\text{-1}}}\] (b) Acceleration, \[3\cdot 0\] Acceleration will be maximum when y is maximum, i.e., \[y=a\] \[2\cdot 0\] Max acceleration, \[\text{N}{{\text{m}}^{\text{-1}}}\] (c) Max. speed of the mass will be when it is passing through the mean position, which is given by \[3\cdot 0\]