PEMBAHASAN SOAL OSN IPA SMP TAHUN 2025 | PART 1

Physics Problem 1: Simple Pendulum Frequency
📌 The frequency ($F$) of a simple pendulum is calculated using the formula $F = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$.
⚙️ Given string length $L = 1 \text{ m}$ and gravitational acceleration $g = 10 \text{ m/s}^2$, the amplitude of $5 \text{ cm}$ is irrelevant for frequency calculation as long as it maintains simple harmonic motion.
✅ The resulting frequency is $\frac{\sqrt{10}}{2\pi} \text{ Hz}$.

Physics Problem 2: Motion on a Smooth Inclined Plane
📌 The motion up the smooth inclined plane is Uniformly Decelerated Linear Motion (GLBB diperlambat), where final velocity $v_t = 0$ after distance $s = 1 \text{ m}$.
🧮 The relationship between initial velocity ($v_0$) and acceleration ($a$) is derived from $v_t^2 = v_0^2 - 2as$, resulting in $v_0^2 = 2a$.
⚙️ The acceleration down the incline is found using Newton's Second Law ($F=ma$), where $F = W \sin\theta = mg \sin 30^\circ$. Since $a = g \sin 30^\circ$ and $\sin 30^\circ = 0.5$, the acceleration is $a = 0.5g$.
✅ Substituting $a$ back yields $v_0^2 = 2(0.5g) = g$, so the initial velocity required is $v_0 = \sqrt{g}$.

Physics Problem 3: Simple Harmonic Vibration Function
📌 The general equation for displacement ($y$) in simple harmonic motion is $y = A \sin(\omega t)$, where $A$ is the amplitude and $\omega$ is the angular frequency.
⚙️ The angular frequency $\omega$ is calculated using the period ($T$): $\omega = \frac{2\pi}{T}$.
✅ Given $A = 20 \text{ cm} = 0.2 \text{ m}$ and $T = 0.2 \text{ s}$, $\omega = \frac{2\pi}{0.2} = 10\pi \text{ rad/s}$.
✅ The resulting vibration function is $y = 0.2 \sin(10\pi t)$.

Physics Problem 4: Vertical Motion After Rope Break (GLBB Analysis)
📌 This problem involves two stages of motion after the rope breaks: upward motion with initial velocity $v = 1 \text{ m/s}$ until $v_t = 0$, followed by free fall from the peak height to the ground.
⚙️ Stage 1 (Upward Travel): The height gained ($H_1$) is found using $v_t^2 = v^2 - 2gH_1$, resulting in $H_1 = \frac{v^2}{2g} = \frac{1^2}{2(10)} = 0.05 \text{ m}$ ($1/20 \text{ m}$). The time taken ($T_1$) is $v_t = v - gT_1$, so $T_1 = \frac{1}{10} = 0.1 \text{ s}$.
✅ The total height to fall from the peak is $H_{\text{total}} = 4 \text{ m} + H_1 = 4.05 \text{ m}$ ($81/20 \text{ m}$).
✅ Stage 2 (Downward Travel): Time taken ($T_2$) is found using $H_{\text{total}} = v_{0, \text{peak}} T_2 + \frac{1}{2}gT_2^2$, where $v_{0, \text{peak}} = 0$. Solving $81/20 = \frac{1}{2}(10)T_2^2$ gives $T_2 = \sqrt{81/100} = 0.9 \text{ s}$.
✅ Total time is $T_{\text{total}} = T_1 + T_2 = 0.1 \text{ s} + 0.9 \text{ s} = 1 \text{ s}$.

Physics Problem 4: Vertical Motion After Rope Break (Quadratic Method)
📌 An alternative method uses a single quadratic equation for the entire displacement from the point the rope breaks until it hits the ground ($y=0$).
⚙️ The equation used is $y = v_0 t - \frac{1}{2}gt^2 + H_0$, where $H_0 = 4 \text{ m}$ is the initial height, $v_0 = 1 \text{ m/s}$ (upward is positive), and $y=0$ at the ground.
✅ This results in the quadratic equation: $0 = 1t - \frac{1}{2}(10)t^2 + 4$, simplifying to $5t^2 - t - 4 = 0$.
✅ Factoring the equation $(5t+4)(t-1) = 0$ yields two solutions: $t = 1 \text{ s}$ and $t = -4/5 \text{ s}$.
✅ Since time cannot be negative, the required time for the ball to hit the floor after the rope breaks is $t = 1 \text{ s}$.

Key Points & Insights
➡️ The frequency of a simple pendulum does not depend on its amplitude ($A$) provided the oscillation is simple harmonic.
➡️ For motion on an inclined plane, the acceleration component parallel to the plane due to gravity is $g \sin\theta$.
➡️ When analyzing vertical projectile motion from a height, using the general displacement equation $y = v_0 t \pm \frac{1}{2}gt^2 + H_0$ allows for solving the total time in one step via a quadratic equation.
➡️ When solving quadratic equations derived from physics, always discard negative time solutions as they are physically impossible in the context of elapsed time since an event.

📸 Video summarized with SummaryTube.com on Feb 08, 2026, 02:12 UTC