Question

Five different spring-mass systems are pictured above, along with the amount of mass hanging from each.
Additionally, a table below gives the spring constant for each spring, along with the amplitude of oscillation after each spring-mass has been set in motion.
What is the rank of the spring-mass systems according to their periods of oscillation, greatest first?

	Spring constant	Amplitude of Oscillation
Blue spring	$20.0N/m$	$15.0cm$
Green spring	$25.0N/m$	$10.0m$
Yellow spring	$30.0N/m$	$20.0cm$
Purple spring	$50.0N/m$	$25.0cm$
Red spring	$60.0N/m$	$5.0cm$

• A. Red, purple, yellow, green, blue
• B. Blue, green, yellow, purple, red
• C. Green, red, yellow, purple, blue
• D. Green, yellow, red, blue, purple
• E. Purple, yellow, blue, green, red

Answer 1

The correct option is D Green, yellow, red, blue, purple

Time period of oscillation $T=2\pi \sqrt{\frac{M}{k}}=a\sqrt{\frac{M}{k}}$ where $a=2\pi$

Blue spring : $T_B=a\sqrt{\frac{1.0}{20.0}}=a\sqrt{0.05}$

Green spring : $T_G=a\sqrt{\frac{5.0}{25.0}}=a\sqrt{0.2}$

Yellow spring : $T_Y=a\sqrt{\frac{3.0}{30.0}}=a\sqrt{0.1}$

Purple spring : $T_P=a\sqrt{\frac{2.0}{50.0}}=a\sqrt{0.04}$

Red spring : $T_R=a\sqrt{\frac{4.0}{60.0}}=a\sqrt{0.067}$ $⟹T_G>T_Y>T_R>T_B>T_P$