Force and Translational Dynamics

What is the primary characteristic of spring forces, making them essential for understanding oscillations?

Which of the following is a characteristic of an ideal spring?

A spring with a spring constant of $k = 50 ,\text{N/m}$ is stretched by $\Delta x = 0.2 ,\text{m}$. What is the magnitude of the force exerted by the spring?

A spring exerts a force of 20 N when stretched by 0.1 m. What is the spring constant of the spring?

Two identical springs are connected in series. If each spring has a spring constant $k$, what is the effective spring constant of the combination?

A spring is stretched a distance $x$ from its equilibrium position. In what direction does the spring force act?

A block attached to a spring is placed on an inclined plane. How does the angle of the incline affect the spring force at equilibrium?

A spring with spring constant $k$ is compressed a distance $x$. If the potential energy stored in the spring is $U$, what is the velocity of a mass $m$ when the spring returns to its equilibrium position, assuming all potential energy is converted to kinetic energy?

A mass is attached to a spring and oscillates in simple harmonic motion. If the spring constant is $k$, the mass is $m$, and the amplitude of oscillation is $A$, what is the total energy of the system?

What is the significance of the negative sign in Hooke's Law ($F = -k\Delta x$)?