Velocity of a Spring?

📌 CONCEPT: Hooke's Law describes the relationship between the force applied to a spring and its resulting displacement from its equilibrium position, with the spring's constant 'k' being a measure of its stiffness.

📐 RULE / FORMULA: According to Hooke's Law, F = kx, where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position. To find the velocity, we can use the formula v = dx/dt = (k/m) ∗ x, where m is the mass of the spring and x is its displacement.

💡 WORKED EXAMPLE: Given that a 2 N force stretches the spring by 2 cm (0.02 m), we can find the spring constant 'k' using the equation 2 = k ∗ 0.02. Solving for 'k', we get k = 100 N/m. Now, if we assume the mass of the spring is m = 0.1 kg, and it is stretched by 0.02 m at time t = 0 s, we can find the velocity of the spring at the instant the force applied is increased from 2 N to 3 N using the formula v = (k/m) ∗ x.

⚠️ COMMON MISTAKE: Students often forget to convert units properly, leading to incorrect values of the spring constant 'k' and subsequently, the velocity 'v'.