Question

15. A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?

The answer is 0.389 kg but please show your work.

Answer 1

Let's look at relationship

$\\ \rm\rightarrowtail T=2\pi\sqrt{\dfrac{m}{k}}$

$\\ \rm\rightarrowtail T\propto \sqrt{m}$

Hence

$\\ \rm\rightarrowtail \dfrac{T_1}{T_2}=\sqrt{\dfrac{m1}{m2}}$

$\\ \rm\rightarrowtail \dfrac{1.5}{2}=\sqrt{\dfrac{0.5}{m2}}$

$\\ \rm\rightarrowtail 0.75^2=\dfrac{0.5}{m2}$

$\\ \rm\rightarrowtail m_2=\dfrac{0.5}{0.75^2}$

$\\ \rm\rightarrowtail m_2=0.889$

Hence

• Mass needs to added =0.889-0.500=0.389kg

Answer 2

Answer

Mass needs to added =0.889-0.500=0.389kg

Explanation: