A 2.4 kg particle undergoes horizontal oscillation at the end of an ideal spring. The displacement-time graph of its motion is shown in the figure. A = [A] m and t3= 0.2 s. Determine the positive displacement x of the particle when it has one‑third of the maximum speed. Express your answer in meters.

A [m] kg particle oscillates horizontally at the end of an ideal spring. The displacement-time graph of its motion is shown in the figure. A = [A] m and t3= [t3] s. When the particle is located at 50% of the amplitude from the equilibrium position, determine its kinetic energy (K) in joules. [Hint: frequency can be determined from the time-displacement graph.]

A mass is attached to a horizontal ideal spring, undergoing simple harmonic motion. The displacement amplitude is A = [A] m. At a certain time t, the potential energy stored in the spring is [E1] J, and the kinetic energy of the mass is [E2] J. Determine the maximum magnitude of the spring force exerted on the mass (in newtons). [Hint: the maximum force in SHM is Fmax = k × A.]

A string is stretched between two fixed points. When plucked at one end, a transverse wave pulse reaches the other end in [t] s. The mass of a 1-meter length of the string is [mu] kg, and the tension in the string is [F] N. Determine the length of the string in meters.

Objects A and B are made of the same material with a density of [rho1] kg/m³. Object A is fully submerged in an unknown liquid, and object B is placed on top of A such that only a fraction [f] of object B is submerged. Given that the density of the unknown liquid is [rho2] kg/m³ and the volume of object B is [vB] m3, determine the volume (in m³) of object A.

A 0.45 kg mass is resting on a vertically oscillating platform. The platform undergoes simple harmonic motion. The displacement-time graph of the platform’s motion is shown in the figure. t2= [t2] s. Determine the maximum oscillation amplitude that allows the mass to stay in contact with the platform at all times. [Hint: the supporting (normal) force becomes zero when the mass is about to lose contact with the platform. Consider that the maximum force in SHM is Fmax = m × amax.]

 A [L] m long string of a musical instrument has a mass of [m] kg. When the string resonates, it forms a standing wave. The figure shows a snapshot of the standing wave at t = 0. The resulting sound wave in the surrounding air has a wavelength of [lamda] m. Calculate the tension in the string (in Newtons) required to sustain this vibration. The speed of sound wave in air is 340 m/s.

A 2.2 kg mass is attached to a horizontal, massless, ideal spring with a spring constant of 30 N/m. The system undergoes simple harmonic motion, and its velocity-time graph is shown in the figure. v0 = [v0] m/s and t2= [t2] s. Determine the amplitude (A) of oscillation in meters.

A solid cube with a side length of [L] m is completely submerged in an oil-filled container and suspended from a scale by a cable. The density of the cube is [rho2] kg/m³, and the density of the oil is [rho1] kg/m³. What is the reading on the scale (apparent weight) when the cube is fully submerged in the oil? Express your answer in newtons (N).

What emotion primarily drove Douglass’s desire to learn how to read?