A pendulum oscillates in a car moving on a horizontal road. If the car accelerates at $a$, the equilibrium position shifts by angle: <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 250 130" style="max-width:250px;margin:0.5em auto;display:block;"> <title>Pendulum in accelerating car — equilibrium tilted by angle θ from vertical</title> <rect width="250" height="130" fill="#faf9f5" rx="6"/> <defs><marker id="ah-jw01q-1" markerWidth="6" markerHeight="4" refX="6" refY="2" orient="auto"><polygon points="0,0 6,2 0,4" fill="#c6613f"/></marker></defs> <circle cx="125" cy="15" r="3" fill="#14140f"/> <line x1="125" y1="15" x2="125" y2="100" stroke="#14140f" stroke-width="0.6" stroke-dasharray="3,3"/> <line x1="125" y1="15" x2="100" y2="95" stroke="#14140f" stroke-width="1.5"/> <circle cx="100" cy="95" r="7" fill="#c6613f"/> <path d="M125,45 A30,30 0 0,0 118,50" fill="none" stroke="#788c5d" stroke-width="0.8"/> <text x="115" y="55" font-size="8" fill="#788c5d">θ</text> <line x1="160" y1="15" x2="200" y2="15" stroke="#c6613f" stroke-width="1.2" marker-end="url(#ah-jw01q-1)"/> <text x="180" y="10" text-anchor="middle" font-size="7" fill="#c6613f">a (acceleration)</text> <text x="125" y="122" text-anchor="middle" font-size="8" fill="#14140f">θ = t$an^{-1}$(a/g)</text> </svg>

The time period of a spring-mass system on the Moon compared to Earth is:

A spring of constant $k$ is cut into two equal halves. The spring constant of each half is:

Two springs of constants $k$ and $2k$ are connected in series. The effective spring constant is:

A mass $m$ is suspended from two springs $k_1$ and $k_2$ in parallel. The time period is: <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 250 160" style="max-width:250px;margin:0.5em auto;display:block;"> <title>Mass suspended from two springs in parallel — both share the same displacement</title> <rect width="250" height="160" fill="#faf9f5" rx="6"/> <line x1="40" y1="15" x2="210" y2="15" stroke="#14140f" stroke-width="2"/> <path d="M80,15 L80,25 L70,30 L90,40 L70,50 L90,60 L70,70 L80,75 L80,85" fill="none" stroke="#c6613f" stroke-width="1.5"/> <path d="M170,15 L170,25 L160,30 L180,40 L160,50 L180,60 L160,70 L170,75 L170,85" fill="none" stroke="#788c5d" stroke-width="1.5"/> <line x1="80" y1="85" x2="170" y2="85" stroke="#14140f" stroke-width="1.5"/> <rect x="105" y="85" width="40" height="30" fill="#c6613f" opacity="0.3" stroke="#14140f" stroke-width="1" rx="3"/> <text x="125" y="105" text-anchor="middle" font-size="10" fill="#14140f" font-weight="600">m</text> <text x="65" y="50" font-size="9" fill="#c6613f">k_{1}</text> <text x="185" y="50" font-size="9" fill="#788c5d">k_{2}</text> <text x="125" y="145" text-anchor="middle" font-size="8" fill="#14140f">k_eff = k_{1} + k_{2}</text> </svg>