Question

Which of the following tables gives information for the spring-mass system in which the mass experiences the greatest maximum acceleration?

• A. $SpringConstant=50N/m,Amplitude=0.25m,Mass=1.0kg$
• B. $SpringConstant=50N/m,Amplitude=0.50m,Mass=1.0kg$
• C. $SpringConstant=50N/m,Amplitude=0.125m,Mass=0.50kg$
• D. $SpringConstant=25N/m,Amplitude=0.50m,Mass=1.0kg$
• E. $SpringConstant=25N/m,Amplitude=0.25m,Mass=1.0kg$

Answer 1

The correct option is B $SpringConstant=50N/m,Amplitude=0.50m,Mass=1.0kg$

Maximum acceleration $a=w^{2}A$ where $w^2=\frac{k}{m}$

$⟹$ $a=\frac{kA}{m}$ $m/s^2$

(A) : $a_A=\frac{50\times 0.25}{1.0}=12.5$ $m/s^2$

(B) : $a_B=\frac{50\times 0.50}{1.0}=25.0$ $m/s^2$

(C) : $a_C=\frac{50\times 0.125}{0.50}=12.5$ $m/s^2$

(D) : $a_D=\frac{25\times 0.50}{1.0}=12.5$ $m/s^2$

(E) : $a_E=\frac{25\times 0.25}{1.0}=6.25$ $m/s^2$ $⟹a_B=a_C>a_A=a_D>a_E$