Final answer:
By applying the conservation of mechanical energy to the system and assuming all kinetic energy at equilibrium position is converted to potential energy at the amplitude, we can calculate the amplitude of oscillation by setting KE equal to PE and solving for A.
Step-by-step explanation:
To find the amplitude of oscillation for an undamped horizontal spring oscillator, we can use the principle of conservation of mechanical energy. The total mechanical energy in a simple harmonic oscillator is conserved and is the sum of kinetic and potential energy. At the equilibrium position, the potential energy stored in the spring is zero, and the entire energy is kinetic.
Using the formula for kinetic energy, KE = 0.5 × m × v2, where m is the mass of the oscillator and v is the velocity at the equilibrium position, we can calculate the kinetic energy at that point. For an oscillator with a mass of 1.57 kg and velocity of 2.93 m/s, KE equals 0.5 × 1.57 kg × (2.93 m/s)2.
This kinetic energy is equal to the maximum potential energy stored in the spring when the mass is at the maximum displacement, i.e., the amplitude A. The potential energy in the spring at maximum displacement is given by PE = 0.5 × k × A2, where k is the spring constant.
Equating the kinetic and potential energies and solving for A gives us A = √(2 × KE / k). By substituting the values into this expression, we can calculate the amplitude of the oscillation.