Answer to Question #1357 in Mechanics | Relativity for Jon ALlen

Question

A block of unknown mass is attached to a
spring of spring constant 9.6 N/m and undergoes simple harmonic motion with an amplitude of 14.8 cm. When the mass is halfway
between its equilibrium position and the end-point, its speed is measured to be 32.7 cm/s.
Calculate the mass of the block.
Answer in units of kg.

Answer 1

We can use the law of enegry conservation:
kx₁²/2 = kx₂²/2+ mv²/2
where
k = 9.6 N/m, x1 = 14.8 x 10^-2 m , x2 = 7.4 x 10^-2 m, v = 32.7x10^-2 m/s²;
so
m = k(x₁²-x₂²)/v² = 9.6 (14.8² - 7.4²)/32.7² = 1.47 kg.