Question

A $1kg$ block attached to a spring vibrates with a frequency of $1Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in a parallel to an $8kg$ block placed on the same table. So, the frequency of vibration of the $8kg$ block is ;

• A. $\frac{1}{4}Hz$
• B. $\frac{1}{2\sqrt{2}}Hz$
• C. $2Hz$
• D. $\frac{1}{2}Hz$

Answer 1

The correct option is D $\frac{1}{2}Hz$

$f_1=1Hz$

$T_1=2x\sqrt{\frac{m_1}{k}}=\frac{1}{f_1}$

$2x=\sqrt{\frac{m}{k}}=1$

$2x\sqrt{\frac{1}{k}}=1$

$\frac{1}{k}={\left(\frac{1}{2x}\right)}^2$

$k=4x^2$

In parallel,

$k_{eq}=k+k=2k$

$T=2x\sqrt{\frac{m_2}{k_{eq}}}=2x\sqrt{\frac{8}{2k}}=2x\sqrt{\frac{8}{8x^2}}=2$

$f=\frac{1}{2}Hz$